What number would you add to both sides of x² + 7x = 4 to complete the square?

Solution:

Given equation x² + 7x = 4

We use the method completing the square to solve such equation.

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 + 7x = 4, the coefficient of the x term is 7. So (7/2)² = 49/4

⇒ x² + 7x +49/4 = 4 + 49/4

⇒ {4x² + 28x + 49}/4 = {16 + 49} /4

⇒ {4x² + 28x + 49} = 16 + 49

⇒ (2x + 7)² = 65 [since a²+ 2ab + b² = (a + b)²]

⇒ (2x + 7)² = (√65)²

This looks like a perfect square, hence 49/4 should be added on both sides.

What number would you add to both sides of x² + 7x = 4 to complete the square?

Summary:

The number 49/4 should be added on both sides of x² + 7x = 4 to complete the square.