Math Help

Posts Tagged ‘quadratic formula’

This section of Math Help online shows you the proof of Quadratic Formula. The Quadratic Formula is very important and should be learned. 

The proof of Quadratic Formula

If ax ² + bx + c = 0 

Then diving the above quadratic equation by a gives: 

Re arranging the above quadratic equation gives: 

 

Here comes the neat trick to solve this quadratic equation, add b 2 / 4a 2 to both sides of the quadratic equation in order to complete square on the left hand side. This gives the resulting quadratic equation: 

 

Then factorizing the left hand side of the quadratic equation gives: 

 

Re-arranging the right hand side of the quadratic equation gives: 

 

Then it is a matter of taking square root of the right hand side and rearranging the quadratic equation as shown below: 

Here we will discuss the famous math quadratic formula for Solving Quadratic Equations. The quadratic formula is very useful and using the quadratic formula is probably the easiest way to solve any quadratic equations as we shall demonstrate soon. The quadratic formula allows you to solve any quadratic equations in the following form.

How to solve Quadratic equations?

Quadratic equations are presented in the form:

In another word, a, x squared, plus, b x, plus c equals zero AND a is not equal to zero where:

• a is the coefficient of x squared,
• b is the coefficient of x and
• c is a constant.

Any quadratic equations can be re arranged into this form. Once we have the quadratic equation in this form, the quadratic formula for calculating x is given by the following.

Quadratic formula

Since any quadratic equations has two solutions, x is given by:

• negative b plus the square root of b squared minus 4 times a times c all divided by 2 times a, and
• negative b minus the square root of b squared minus 4 times a times c all divided by 2 times a.

Now you can solve any quadratic equations. But, just to make sure that you can, we are going to do an example of how to solve a quadratic equation. Let’s solve a simple quadratic equation below.

Example of solving quadratic equation

Now we can re arrange to equation so that it is in the form a, x squared, plus b x, plus c as follows:

Now you can see that a = 1, b = -1 and c = -6.

So, plugging a, b, and c into the quadratic formula, we have:

In another word, x is either 3 or -2. That’s it. Now you know how to solve a quadratic equation.