How do we solve quadratic equations by completing the square?

Okay, so first let's review quadratic equations and how to solve them.

How does a quadratic equation look like? And how do you solve them? 

Well a quadratic equation is an equation that has an exponent of two inside the equation. And in order to solve it, you have to plug it in into the following formula:

                             

So let's say you have the following equation: 3x^2+6x-7=0 All you have to do is plug in a,b, and c into the quadratic formula to find x. REMEMBER THAT YOU WILL ALWAYS GET TWO ANSWERS FOR A QUADRATIC EQUATION!  

Now that you know how to solve a quadratic equation, here's a little story for you to read:

      

Okay, now let's take it a step further and instead of just plugging the equation into the formula, what if you're asked to complete the square? :o

No worries, it's quite easy. 

First let's take an equation.

Here you go --> 2x^2+8x=10

Divide the whole equation by 2 to get x^2+4x=5 

Then you have to divide the bx term by two to get 2 and then square it to get 4. This will now be your c term and you will have to add this to the other side. You will end up with x^2+4x+4=9. You have completed the square! :D

So just to sum it all up, here are the steps you should follow for any problem in which you have to solve a quadratic equation by completing the square:

Step 1: Put the variable terms on one side of the equation and the constants on the other side. Make sure the coefficient of the squared term (a) is 1.

Step 2: Find the value that will complete the square by taking half of the linear term coefficient (b) and squaring it. 

Step 3: Add the value to each side.

Step 4: Factor the perfect square.

Step 5: Solve by taking the square root of both sides.