What constant term should be used to complete the square? x² - 5x + _____ = 7

Solution:

Given equation x² - 5x =7

Let us solve this by completing the square.

Divide the coefficient of the x term by 2 then square the result.

This number will be added to both sides of the equation.

For the quadratic equation x² - 5x =7, the coefficient of the x term is -5

So (-5/2)² = 25/4

⇒ x² - 5x + 25/4 = 7 + 25/4

⇒ {4x² - 20x + 25}/4 = {28 + 25} /4

⇒ {4x² - 20x + 25} = 28 + 25

⇒ (2x - 5)² = 53 [ since a² - 2ab + b² = (a - b)²]

⇒ (2x - 5)² = (√53)²

This looks like a perfect square, hence 25/4 should be added on both sides.

What constant term should be used to complete the square? x² - 5x + _____ = 7

Summary:

The constant term that should be used to complete the square? x² - 5x + _____ = 7 is 25/4.