What number should be added to both sides of the equation to complete the square? x² + 12x = 11

Solution:

For completing the square in a quadratic equation, we perform the following 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 x² + 12x = 11 the coefficient of the term x is 12

(12/2)² = 36

The given equation can be written as

 x² + 12x + 36 = 11 + 36

x² + 12x + 36 = 47

We can write it as

(x + 6)² = 47

Take square root on both sides.

|x + 6| = √47

We get

x = 6 + √47

In other case,

-x + 6 = √47

x = 6 - √47

Therefore, 36 should be added to both sides of the equation to complete the square x² + 12x = 11.

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What number should be added to both sides of the equation to complete the square? x² + 12x = 11

Summary:

The number that should be added to both sides of the equation to complete the square x² + 12x = 11 is 36.