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 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 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.