# How to Complete the Square

## Completing the Square

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 **x ^{2}** and

**x**terms only.

We can complete the square on these terms, replacing them with a squared binomial minus a number.

# 2

Replace the **x ^{2}** 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).

2^{2} = 2 × 2 = 4

Write it in the gap after the **−** sign.

**Don't forget:** The answer from **Step 5** (2) comes from dividing the coefficient of **x** (4) by 2.

# 8

Consider the whole of the equation.

# 9

Add the numbers outside of the brackets together.

− 4 + 6 = 6 − 4 = + 2

### Answer:

We have completed the square on the quadratic equation: