# What number should be added to both sides of the equation to complete the square?

x^{2} + 3x = 6

**Solution:**

For completing the square, we follow these steps:

- First, divide the coefficient of the term x by 2 and square the result.
- This number should be added to both sides of the equation

For the equation x^{2} + 3x = 6 the coefficient of the term x is 3

(3/2)^{2} = 9/4

The given equation can be written as

x^{2} + 3x + 9/4 = 6 + 9/4

x^{2} + 3x + 9/4 = 33/4

We can write it as

(x + 3/2)^{2} = 33/4

On both sides take square root

|x + 3/2| = √33/4

We get

x = 3/2 + √33/4

In other case,

- x + 3/2 = √33/4

x = 3/2 - √33/4

Therefore, 9/4should be added to both sides of the equation to complete the square x^{2} + 3x = 6.

## What number should be added to both sides of the equation to complete the square?

x^{2}+ 3x = 6

**Summary:**

The number that should be added to both sides of the equation to complete the square x^{2} + 3x = 6 is 9/4.