A Guide to Completing the Square

Description

This video is a tutorial 0n how to solve quadratic equations by completing the square. Two example problems are provided in the video and worked through. The entire process of completing the square is explained in this video.

Overview

A quadratic equation is probably the most well-known type of math problem, following the form ax^2 + bx + c = 0. Most people already know one way of solving these types of equations – the quadratic formula. But the quadratic formula is only one of 3 methods that can be used. The method discussed here is completing the square. Completing the square is when you turn an equation into a squared binomial in order to solve it. You need to remember this:

(x + a)^2 = x^2 + 2ax + a^2

You need to make your equation match up to this. Take the middle term and divide it by 2. That number is a. Square a – if you get the number on your trinomial, then this is a perfect square. You want it to be a perfect square. If it is not, you must get rid of the number on the end and move it to the other side by addition or subtraction. Then you will need to replace the number with a^2 – you will add this to both sides. You find out the value of a the same way you did earlier. You will eventually come up with something that looks like this:

(x + a)^2 = n

Now you will take the square root of both sides, and subtract a from both sides. Then you will be left with x, and it will tell you what x equal. Remember, when taking a square root you must put plus/minus in front of the square root! Just like in the quadratic formula, you need a +/- in your answer.