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# What number would you add to both sides of x^{2} + 7x = 4 to complete the square?

**Solution:**

Given equation x^{2} + 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 x^{2} + 7x = 4, the coefficient of the x term is 7. So (7/2)^{2} = 49/4

⇒ x^{2} + 7x +49/4 = 4 + 49/4

⇒ {4x^{2} + 28x + 49}/4 = {16 + 49} /4

⇒ {4x^{2} + 28x + 49} = 16 + 49

⇒ (2x + 7)^{2} = 65 [since a^{2}+ 2ab + b^{2} = (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 x^{2} + 7x = 4 to complete the square?

**Summary:**

The number 49/4 should be added on both sides of x^{2} + 7x = 4 to complete the square.

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