# What number should be added to both sides of the equation to complete the square? x^{2 }- 6x - 13 = 0

**Solution:**

We will express the given equation in the form (x - a)^{2} = 0.

Let us see what could be added to both sides of this equation to complete the square.

On expanding (x - a)^{2} = 0, we get x^{2} - 2ax + a^{2} = 0

On comparing x^{2} - 2ax + a^{2} = 0 with x^{2 }- 6x - 13 = 0, we get -2a = -6.

This means the value of a is 3.

Now, we have to decide a number that should be added to both sides of equation x^{2 }- 6x - 13 = 0 to make LHS equivalent to (x - 3)^{2}.

x^{2 }- 6x - 13 = 0

(x)^{2 }- 2 × (x) × 3 = 13

If we add (3)^{2} on both sides, we get,

(x)^{2 }- 2 × (x) × 3 + (3)^{2} = 13 + (3)^{2 }

x^{2 }- 6x + 9 = 13 + 9

(x - 3)^{2} = 22

Therefore, we should add 22 to both sides of the equation x^{2 }- 6x - 13 = 0 to complete the square.

## What number should be added to both sides of the equation to complete the square? x^{2 }- 6x - 13 = 0

**Summary:**

The number 22 should be added to both sides of the equation x^{2 }- 6x - 13 = 0 to complete the square.

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