Learn and Use Quadratic Formula with an Example

Mathematics is quite tricky but an interesting subject.  It is full of equations and calculations that have much significant importance in different fields. Learning this subject is very useful to excel in various fields and also to clear many competitive exams.  So, today we will learn about a simple yet useful topic that is quadratic equations. To solve any quadratic equation you need to know its formula and steps to use the quadratic formula. In this article, you will get the introduction of quadratic equations along with its different forms and examples.

Quadratic Equation

Quadratic equation – its introduction

It is a second-degree equation that means it has at least one term with a square. The equation is always defined in its standard form. The standard form of this equation is ax² + box +c = 0 where a, b and c are the constants or coefficients. In this equation, there is a variable that is ‘X’ with an unknown value. Rest of the coefficients has known value. Using the quadratic formula, we usually find the value of this unknown variable. An equation is called quadratic if:

·         Its first variable that is ‘a’ is not equal to zero while the other variables can be zero.

·         The third variable is constant or an absolute term.

·         It must be a second-degree equation.

·         Value of unknown variable, i.e., x must satisfy the equation and hence called the root of an equation.

To understand what the quadratic equation is, here are examples of quadratic equation in its different form.

·         Standard form equation: 3x2+4x-12=0

·         Equation without the linear coefficient: x²-8=0

·         Equation without constant: 2x2+ 16x=0

·         Equation in factor form: (x+2) (x-4) =0

·         In another form: x(x-2) = 8, on multiplying and moving eight the equation comes in standard form and becomes x²-2x-8=0

These were some of the examples of quadratic equation in its different forms. Let’s see the procedure to solve these equations. Using a quadratic formula you can solve any quadratic equation, you can also use the other method where equate the factor to zero and get the value. But this method does not work for every problem as sometimes it can be quite messy because it does not get factored. The formula for the standard equation is:

                                                                     x= (-b±√ (b²-4ac))/2a

To use this formula, first, arrange the equation in the standard form.  Remember that the coefficient b will get squared completely means along with the sign. On solving the problem, you will get two roots, one with a positive value and other with the negative value. Take an example to understand the formula.

For example:

To solve x²+2x-4=0 , You can find the factor or simply put the values of a, b and c in the above formula to get the answer. Let’s solve using the quadratic formula.  The value of coefficients a, band c is 1, 2 and-4 respectively. Put them in the formula.

x= (-2±√ (2²-4.1.-4))/2.1

= (-2±√(4 +16))/2

= (-2±√20)/2

= (-2±2√5)/2   

The two roots of equation are -2+2√5/2 and -2-2√5/2

If you understand this example, then try solving other problem as well. Go with the simple problems and then move toward the tough questions. I hope you understand how to use the quadratic formula.

Types of Equations

Algebra, as a topic in mathematics. Is being tacked right from primary school up to the highest level of learning. If you ask a junior mathematician what they understand by the term algebraic equation. A good number of them will give out an example that looks like this; 2x + 3x + 4x=. Yes, this is a form of an algebraic equation. I cannot refute since when you work on it, still you will come up with an answer. Many of the mathematicians have tackled some equations, but in the real sense good percentages of them do not understand or are well conversant with the types of equations. Funnily, some can never know the types of equations, but they can freely work on problems from varied types of equations.

Equation

Variables and constants when put together form an algebraic equation and it must have a symbol of equality to qualify as an algebraic equation.  Therefore an expression having the equal sign (=) is referred to as an equation. For example; 4a + 3b +7c = -7. With this rough background information. Let us discuss the types of equations that we are likely to encounter in any test or article:

1)    Linear Equations:

In this type of equation, the terms can be a constant or the product of a constant and one variable. A straight line kind of graph is as a result of two variables. Equation having two variables usually have a formula as; y = mx + c,

M is referred to as slope while c is the point at which it intercepts the y-axis.

2)    Radical Equations:

This is a very common type of an equation. How can you identify a radical equation? Very simple, if you see a square root sign anywhere accompanying the equation then it’s a radical equation. Radicle equations on many occasions are being handled by mathematicians at the secondary level of learning.  Below is an example of a radicle equation;

 √x+14=28

Have you tackled such kind of equation?

3)    Quadratic equations:

When you see or hear the term Quadra, what comes into your mind? Many of us will think about four in the first case. Yes grammatically Quadra, means four. Mathematically we have the quadratic equation. This type of equation in which one variable has got the variable with an exponent of 2. It usually has a structure like this, ax² + bx + c = 0, a ≠ 0 for example;

4x² + 6x – 74 = 0 is an example of a quadratic equation.

4)    Rational Equations:

Such kind of equations deals with rational expressions. The term rational expression may sound unfamiliar, yet you know it right? Let me shade some light. A rational expression is a fraction in which both the numerator and the denominator are polynomials.

X2/2 = X+2/4

These types of equations may tend to be hectic to solve. Why? Because they consume a lot of time as some involve the collection of like terms together in order to move on. But with factor calculator, all is made easy.

How to Solve a Quadratic Formula

Before even diving into any calculations, we need to know what a quadratic formula is. It is a formula one of the formulas that is being used to solve a quadratic equation. This formula always comes in handy where other formulas like factoring, completing the square method, or graphing may not really yield the expected results. It is the best and the most convenient way of solving quadratic equations. This formula was derived by Pythagoras and Euclid. They are world famous mathematicians of all time.

So, how does quadratic formula looks like?

If you have ever come across something like this: 

Then you may or may not have known that this is a quadratic equation. This formula is normally derived from the equation 

So, “x” is obviously the variable we are trying to solve, while a, b and c are just mere numbers. Actually, they are the numerical coefficient of the quadratic equation you have been given to solve.

Like for example: 

Here, the value of a will be equal to 3, while that of b will be equal to 10, and c will have a value equals to 8.

If you do not know how to solve this equation or you would like to know more on how to derive the quadratic formula, quickmath.com has a better way of helping you in understanding it. It has so many examples that you can choose to follow or ignore them if you want. But, I bet you will be the best mathematician after going through their step by step examples and doing some of the exercises that you may come across along the way.

Want to try solving an equation using quadratic formula?

We don’t have to look for some quadratic equations online. We can just use the one above.

So we know that quadratic formula is

Therefore, we will just substitute the values of the given equations here but appropriately. We will end up with something like this

This should be 

Therefore x = - 2 or x = - 1.333

If you substitute the x, in the quadratic equation, with -2 or -1.333 you will find that the final values at Right Hand Side and Left Hand Side will be equal. With this, you can use comfortable brag to your friends that you a good mathematician and that you can solve almost any quadratic equation that crisscrosses your path during exams.

For you not to forget the formula and how it works, make sure you keep practicing it almost on a daily basis. Go through many sample equations, exercises and also past papers. If you do not do this, you may end up going back to square one. If that happens, you can always redeem yourself from the website qucikmath.com.

Wish all the best in your online math classes, and good luck in your exams or Continuous Assessment Tests or any term paper you have been given by your tutor or lecturer or teacher.

Solving Math Problems Like a Pro

For the longest time, I have known people who have tried their best to do away with math. For them it is a big, scary, complicated, monster that would cause nightmares day or night. Funny as it sounds, this is true to most students, even adults. They think math is a series of problems that need to be answered. However, they got it all the other way, because math is the solution to most of the available numerical problems. It is even part of our daily problem solving tasks.

Math Solver

Nevertheless, why do they feel this way, because the process and scrutiny of deriving an answer from a series of math problems is a whole lot of work? It takes time and effort that could be used for other life priorities. Finding a better and faster way of solving these math equations will make them realize that Math is indeed a solution and not a problem.

Are you fond of watching investigative movies and series? It really amazes me to see cases being solved by an individual or a group through a step by step process. And now, it even gets more interesting due to the advancement of technology. They can hastily solve issues and cases with the use of new inventions, discoveries and solutions. Math and algebra are no different. It is just like crime or scene solving puzzle, which needs to be solved by a step by step process. But if these criminal fighters are into advancement, why not us? We can also solve algebraic problems through the advancement of technology and the internet.

Take the online math solvers. These sites are designed to make crime solving, I mean math solving easy and simple. It includes process that could come up with an answer in a couple of minutes unlike the manual way that could take long hours of computation. If this is really a case, the suspect has already fled and the victim is already dead, right? That is why we have to learn how to adapt and move fast.

Amazingly, these sites do not charge for anything. You can solve algebraic equations with the use of their specialized calculators. It also covers a wide range of algebra from basic expressions, fractions, expanding, factoring and quadratic equations. This can help save lots of time and headache right?

Try solving this equation,   (9*x-3)*(6*x-7) = (18*x-1)*(3*x+2)-1
The answer is x = 4/19
How much time did you spend computing? Were you able to come up with the right answer? Did you know the solution immediately or you were lured into trial and error? Did you know, with www.quickmath.com (an algebra solver site) it only took 10 seconds?

For the math lovers, do not worry this is still math in the new era. Besides, the logic and equations behind these sites still depended a lot with the traditional math. Now, why don’t you try it yourself and discover the benefits of adapting to change. Let us make our life simpler to achieve greater things.