Saturday, August 26, 2017

Quadratic Formula : A Better way of Solving Quadratic Equations

Algebra is regarded as the most important part of mathematics. There are many interesting topics in algebra that you may get to learn. However quadratic equations are known to be some of the most common discussions among the learners. There can be many different ways to solve quadratic equations well. However, with the need of some easy methods, the emergence of the quadratic formula is considered to be great. There are many important things that you may need to know about this topic in order to be perfect in it. Here, we are going to discuss some easy ways of solving problems for the beginners.

Quadratic Formula

Significance
There are many different types of methods and formula that are used to solve equations whether linear or quadratic. However, there can be many complexities associated with the solutions of the quadratic equations however there have been many other formula that are designed specially to make this procedure easy. Some quadratic equations cannot be factored readily because of different reasons. Therefore you need to take up certain necessary steps so that the equation is ready to be factored. You can also choose to factor the trinomial and then use the square root property to solve the equations.  

However, all these factoring and finding the square root will make the solution lengthy and more confusing for the student. Therefore the best way to simplify the solution is to use the quadratic equation for getting the answer. We will further learn about the use of the formula and also what it exactly is. 

The formula is the simplified form of the complete result that you may get through the factoring of the trinomial. The formula is: 
For a trinomial that is in the form ax² + bx + c = 0. Thus with this, you can simplify the solution for your problems and get the right answers in the least time with least efforts.

Clear the concept
Now understand in deep, recall the steps that were involved in completing the square for the equation. We will do it by completing the square of the general equation i.e.
ax² + bx + c = 0 and see how the formula came into existence.
·         It starts from the equation x² + bx + c = 0
.
·         Now rewrite so that the variable is isolated to one side: .x² + bx 
·         Add (b/2)²
 to both the sides and complete the square.
·         Now solve for the value of x after rewriting the square of the binomial. 
 
Thus you just need to learn a single formula, and you can eliminate the so many long processes involved in the solution to get the right answers. This way you will always be able to solve the quadratic equation in the best way and also get the right answers at once. There are many more interesting things that you will get to know as you practice for the formula. Therefore from the above discussions, it can be said that the quadratic formula is a no different concept. It is just the summarized form of the complete steps involved in solving the quadratic equations. Therefore it is better to use this to solve the algebraic problems rather than using long steps and getting confused. 

Tuesday, July 18, 2017

Get perfect in Solving Equations: Know some important points

Mathematics is one of the most interesting subjects from the academic courses. There are many interesting facts that are known to constitute mathematics. Algebra is known to be one of the most important aspects of mathematics that you need to learn. Algebraic equations, therefore, stand to be some of the most basic concepts here. There are many interesting tricks that can be related to the solution of these algebraic problems. They are known to make the process of getting the solution much easier than before. This also helps the students to learn the concepts well. There can be many different aspects that will affect the methods used for solving equations.   
Solving Equations
Solving Equations

We will discuss some of those here and help you to get the best answers with the best tricks. However, you first need to know that there are many different types of equations. Therefore the ways to solve them will also be different to an extent. The use of these methods needs to be clear in order to be perfect in solving equations. There are considerably many different algebraic concepts that you may need to learn. However, you first need to understand that addition, subtraction, multiplication, and division are some of the most basic pillars that will help you to be perfect. If you are good at these, then you will be absolutely good at solving them.

Steps to get the solution
Algebraic problems are those who need to be solved as per correct steps. Step by step solution will always bring you the right solution. So make sure that you try to cover each step perfectly. However, there are many important steps involved in the solution of an algebraic equation. Here are the steps explained and illustrated for you:

Write and observe the equation: You need to know the equation that is to be solved, write it on the sheet and pick up all the important aspects of it. For example, the equation is: . Note down all that factors in this that you feel are important.

Simplification of the equation: The next step is to simplify both the sides of the equation. However remember the concept of LHS and RHS always. This is the most important concept here. You need to bring the variable to one side and the rest of the equation to the other. For example:

x² + 513= 1023;
x² = 1023-513; Therefore,
x = √510
This is the simplified form of the equation.

Apply the formula: Once you have simplified the equation you need to apply the required formula. This may not be the case in linear equations however as these can be solved easily by using the different operations. However, there can be some different cases too. Therefore you need to know how to deal with the different problems. You need to make use of the correct formula otherwise it may not work sometimes. With these tips, you will be able to solve equations in a better way. Also with considerable practice, you will be able to get perfect in solving equations with any level of difficulty.  

Thursday, June 15, 2017

Factoring Polynomials – How to Factor Polynomials?

Factoring is an important term in mathematics which let you to fi9nd t6he products of a polynomial. Well, you will need to practice this as it is easy, but without practice, one will not be able to understand its pattern.  For factoring polynomials, one should be excellent at factoring numbers plus must have the basic knowledge of algebra. So, today, we are looking for the methods for factorizing these polynomials and convert it into a binomial. 

Steps to factories polynomials
Yes, you need to learn steps as one should know as which to do at first to factories it. The most significant term included in it is Greatest Common factor which is an abbreviation of GCF. 
·         In the first step, you need to find out the greatest common factor.  If you don’t know what GCF is, then let me tell you that it is the biggest expression that will be common in all the terms. In other words, while solving polynomials, one has to find a number which must be a common factor or number in all the terms from which it is obtained.
·         In case you will get a trinomial in which the equation contains three terms and for4 solving that terms one can take help of a FOIL method.

·         In case, it is a binomial one should look for the sum of cubes or different of squares. And after you factories all the polynomials then one has to use zero as a product property to find the answers.

 Now, let’s factorize polynomials with an example. Let’s solve equation 

So, let’s start answering it:  

Now, in the next step, consider 10 and factorize this number. After you finish factorizing it, you will get 5 and two from it.
Now, 
Well, we write (5x) and (-3x) to factorize these polynomials. Besides his, always make sure that you will put right sign before the number as a single wrong sign will give you the right answer. Besides this, you need to know all the rules of signs.
Now, you have to take common x from the equation like:  

Now, after this whole calculation, you have to take zero products for finding out the value x. Now,
x+5=0 which will give you x = -5 and (x-2) will give you, x=2.
So, this is the entire solution of the trinomial equation. Well, there are still various things which you should consider while factoring polynomial:
·         Make sure that you learn about the signs at first because using proper sign is an essential part of the solution.
·         Remember this common rule of signs: 




·         Besides this, arrange the middle terms in a way that its sum will be equal to the last term and its product will be equal to the middle value of the equation.

Factoring polynomial is full of fun, and when you get used to it, and then you will love to solve such problems. Math is just full of fun when you start understating its concepts.

Saturday, June 10, 2017

Know a Simple Method for Adding Fractions with Same Denominators and Different Denominators

You may have come across with fractions often since you are studying the factions. They come in the formulas, algebraic equations, and some practical problems. Algebraic equations contain fractions, so it is an important topic to solve the equations of algebra. You should study about adding fractions that contain algebraic expressions.  However, numbers are included in the fractions of arithmetic. You should know all the operations on fractions as they are useful for various problems. You must be capable of solving addition, subtraction, division and multiplication of different fractions. Here, you will study how to add two different fractions that are containing only numbers by an easy method.

Adding fractions
Adding fractions 

Types of fractions
Firstly, you should be aware of the different types of fractions. There are usually two kinds of fractions used that are like or same fractions and unlike fractions for addition. The like fractions are the fractions that have the same number at the denominator place like 2/3 and 4/3. Whereas, the, unlike fractions, has different numbers at the denominators place like 2/3 and 4/11. You should able for adding fractions of both like and unlike fractions.

To add the like fractions
To add two different fractions having same denominators is simple. You have to add only the numbers at the numerators of both the like fraction. After adding the numerators, check whether it can be simplified further or not. If the fraction can be simplified that is it can be reduced, you should correctly convert it into lowest form. It is explained in the example below.

So, as the both the denominators are same, you can add it as, 




It can be reduced further as both 4 and 8 are divisible by a common number that is 4. Thus, the correct answer to this problem will be,  

To add the unlike fractions
To add two unlike fractions is little tricky, as the denominators are not same. In this case, you have to make the denominators of the fraction same. So convert the fractions so that they have the same denominator and then simply add them. For adding fractions easily, you must ensure sure that both the bottom numbers that is denominators are same.
    Firstly, convert the unlike fractions to like fractions by making both the denominators same.
    Then, you have to add only the numerators of both the fractions, as the denominators are made same.
    Then, if the fraction obtained after addition can be simply further, you must convert it into lowest or reduced form correctly. it will be your final answer that would be a fraction.

Consider this problem to understand it better, and you can easily add the fractions.
Firstly, you have to make both the denominators same as they are different that are 3 and 6. If we multiply both the numerator and denominator of the first fraction by 1/3 by 2, it can be converted to 2/6. So, you can add this new fraction with the second fraction 5/6 that gives the answer as 7/6.
So, you have studied to add the arithmetic fractions. Adding fractions in the way to add two algebraic fractions is also simple for you.

Wednesday, May 24, 2017

The Quadratic Formula - An Easy Way to Solve Quadratic Equations

Algebra has been one of the most important parts of mathematics. And the quadratic formula has been one of the most important aspects of algebraic math. There are many ways of solving a problem through this formula however you always require some tips for the best solutions. Mathematics is a subject which requires lots of practice. Also, math is known to hold an important place in all types of exams. Therefore you require some perfect tricks to solve the mathematical problems with ease and more accurately. Therefore here we will be discussing something about this.

The need for tricks  
Shortcut tricks are very important to excel in competitive examinations. These tricks will help you to manage time well and solve the problems in few easy steps. Therefore it is very important to practice some short tricks in order to get better in the subject. While practicing, you are always advised to go through the problems thoroughly. Before starting up with these, you are suggested to note down twenty problems related to quadratic equations. Now practice some problems which involve basic issues and keep track of time while doing this. This way you will be able to learn time management in a better way.

Solve a problem now
Often, one of the simplest ways of solving “ax2+bx+c=0 ” for finding the value of x is, factoring the quadratic. You should set all the factors equal to zero first. But this way of solving gets messy sometimes. Therefore to make the solution easy there is the quadratic formula. This can help you to find the solution in the best way. This formula uses “a”, “b”, and “c” from “ax2+bx+c ”, here “a”, “b”, and “c” are constants and x is a variable. These are the numerical coefficients you are given to solve. 
The formula is: for 

For the formula to work efficiently, you need to arrange the formula in the form “(quadratic) =0”. Also, “2a” in the formula is taken to be underneath anything mentioned above it. This also includes the square root.   

Example: Solve  x2 = 3x-4= 0

First of all, we will factor the quadratic equation: x2=3x-4=(x=4) (x-1)=0
Now we will try to apply the formula to solve this equation. Using a=1, b=3, and c=-4. Then the solution would look something like



Solving this further we will get: 



Further, this gets reduced to: 








Therefore we get the expected values as x=-4 or x=1.

Thus using the formula, you can complete solving the problems very easily. Therefore you may have got the best solutions for your queries in solving the quadratic equations. Thus it may be clear to you that with the use of this formula you can make the problems to be really easy.  Therefore it can be said that there are many advantages associated with the use of the quadratic formula. Also these can be applied to the problems to get the accurate solutions very easily.

Sunday, May 7, 2017

Want an Answer for Variable X?

Let me start by explaining what a variable means in mathematics. A variable is something that has its value changing constantly. One minute it is value say 10, the next minute its value has changed to some random number like 23. That is why it is called a variable; deduced from the word varying.

How to Solve for x

Now that you have understood what a variable means, let us dive in straight in to getting the values for that variable. If you do not know how to do it, you can jump into quickmath.com. There, you will find so many steps on how to solve for x.


For example, given a simple equation like the one below, 3x + 3= 0
, And you are told to solve for x
Steps that you will see at that website will be like the one I am about to show you.
Here we go,

Step 1:   You need to collect the like terms together. That is, in an equation, the set that has variables are like terms same case to those that do not have variables.
In our case, 3x will remain on the left hand side (L.H.S) while taking the 3 to the Right Hand Side (R.H.S).
You will get; 3x = 0 - 3
Remember, once a quotient crosses over to the other side of the equal sign, its + or – symbol has to be interchanged. That is why, you see +3 changing to being -3,


Step 2:  You go ahead to start simplifying it. That is, 3x = -3

Step 3:  make sure you remain with the variable on one side. Therefore, you will have to divide it by 3 like this;



When you do the division, you will find that the value of x will be -1. i.e. x = -1

Complex example

Solving variable x has its own difficulty levels. Simple equations like the one, I just illustrated above are less difficult to solve. At times, you may come across a complex equation and are told to find the value of variable x in that equation. If you know nothing, you may start sweating profusely like African pot on fire. Anyway, just wanted to let you know that there is a way you can stop this swearing before it even occurs. I will stick with quickmath.com as the best math friend you can have who will offer his relentless services to you for free.
From there, you can get to know how to solve for x in sophisticated equations like this one;

Okay, for math geniuses, I know they will say that this is a simple equation. However, not everyone agrees with them. I, for one think that this equation involves a lot of thinking. Though the equation could be cumbersome and time consuming, you will eventually land at the answer. The value for x in our case should be 1.775 having rounded it off to the nearest thousandths.
If your answer is different from mine, you need to retrace your steps and see where you went wrong.