# What constant term should be used to complete the square? x^{2} - 5x + _____ = 7

**Solution:**

Given equation x^{2} - 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 x^{2} - 5x =7, the coefficient of the x term is -5

So (-5/2)^{2} = 25/4

⇒ x^{2} - 5x + 25/4 = 7 + 25/4

⇒ {4x^{2} - 20x + 25}/4 = {28 + 25} /4

⇒ {4x^{2} - 20x + 25} = 28 + 25

⇒ (2x - 5)^{2} = 53 [ since a^{2} - 2ab + b^{2} = (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? x^{2} - 5x + _____ = 7

**Summary:**

The constant term that should be used to complete the square? x^{2} - 5x + _____ = 7 is 25/4.

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