What number should be added to both sides of the equation to complete the square?
x² + 8x = 4

Solution:

The following are the steps taken to complete the square while solving a quadratic equation :

• 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 x² + 8x = 4 the coefficient of the term x is 8

(8/2)² = 16

The given equation can be written as

x² + 8x + 16 = 4 + 16

x² + 8x + 16 = 20

We can write it as

(x + 4)² = 20

On both sides take square root

|x + 4| = √20

We get

x = 4 + √20

In other case,

- x + 4 = √20

x = 4 - √20

Therefore, 16should be added to both sides of the equation to complete the square x² + 8x = 4.

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What number should be added to both sides of the equation to complete the square?
x² + 8x = 4

Summary:

The number that should be added to both sides of the equation to complete the square x² + 8x = 4 is 16.