The Lesson
Completing the square is a way of simplifying a quadratic equation. Completing the square on a quadratic equation writes it as a squared binomial plus (or minus) a number:
How to Complete the Square
Completing the square is easy.Question
Complete the square on the quadratic equation shown below.
Step-by-Step:
1
Consider the x2 and x terms only.
We can complete the square on these terms, replacing them with a squared binomial minus a number.

2
Replace the x2 and x terms with a squared bracket.
Leave a gap inside the brackets for two terms.
Leave a gap after the brackets for a number to be subtracted.

3
Write an x in the brackets.

4
Look at the original equation.
Find the sign in front of the x term. In our example, it is +.
Write this sign after the x in the brackets.

5
Look at the original equation.
Find the number in front of the x term (called the coefficient). In our example, it is 4.
Divide the coefficient of x by 2.

4 ÷ 2 = 2
6
Write the answer (2) in the gap in the brackets.

7
Square the answer from Step 5 (2).
Don't forget: The answer from Step 5 (2) comes from dividing the coefficient of x (4) by 2.
22 = 2 × 2 = 4
Write it in the gap after the − sign.
8
Consider the whole of the equation.

9
Answer:
We have completed the square on the quadratic equation:
Completing the Square and Perfect Square Trinomials
Completing the square comes from perfect square trinomials.
- A binomial is two terms added (or subtracted) together: x + 2.
-
A squared binomial means multiplying the binomial by itself: (x + 2)2.
(x + 2)2 = (x + 2) × (x + 2)
- A trinomial is three terms added (or subtracted) together: x2 + 4x + 22.

- The number in the brackets (2) is half the number in front of the x (4).
- The number being subtracted from the squared brackets (2) is half the number in front of the x (4) squared (22).