Completing The Square
In this lesson, you will learn how to use the completing the square technique to rewrite any quadratic equation into a more useful form. We will first understand how the formula is derived, then go through three examples to help you apply it step by step.
Related Lessons:
Proving Complete The Square Formula
In this video, we will go through how the completing the square formula is derived. If you prefer understanding Maths at a deeper level, you can use this method instead of simply memorising the formula. The formula for Complete The Square is:
\(x^2+nx+c=\left(x+\frac{n}{2}\right)^2-\left(\frac{n}{2}\right)^2+c\)
Example 1
Write the following equation in the form \(𝑎(𝑥+𝑏)^2+𝑐\)
- \(𝑥^2+4𝑥−6\)
- \(𝑥^2+5𝑥−6\)
- \(2𝑥^2+8𝑥+5\)
- \(4𝑥^2−8𝑥+6\)
Example 2
- Express \(𝑥^2+11𝑥−15\) in the form \((𝑥+𝑎)^2+𝑏\)
- Hence solve the equation \(𝑥^2+11𝑥−15=0\), giving your answers correct to two decimal places.
Example 3
- Express \(−𝑥^2+8𝑥+15 \) in the form \(a(𝑥+b)^2+c\)
- Hence solve the equation \(−𝑥^2+8𝑥+15=0\), giving your answers correct to two decimal places.