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:

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## 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**and^{2}**x**terms only. We can complete the square on these terms, replacing them with a squared binomial minus a number.## 2

Replace the

**x**and^{2}**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

Write it in the gap after the ^{2}= 2 × 2 = 4**−**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

## 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 perfect square trinomial is the result of squaring a binomial.- 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:**x**.^{2}+ 4x + 2^{2}

- 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 (**2**).^{2}

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