What number should be added to both sides of the equation to complete the square? x² - 10x = 7

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 - 10x = 7 the coefficient of the term x is -10

(-10/2)² = 25

The given equation can be written as

 x² - 10x + 25 = 7 + 25

x² - 10x + 25 = 32

We can write it as

(x - 5)² = 32

Take square root on both sides.

|x - 5| = √32

We get

x = 5 + √32

In other case,

-x + 5 = √32

x = 5 - √32

Therefore, 25 should be added to both sides of the equation to complete the square x² - 10x = 7.

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What number should be added to both sides of the equation to complete the square? x² - 10x = 7

Summary:

The number that should be added to both sides of the equation to complete the square x² - 10x = 7 is 25.