# What constant can be added to x^{2} - 6x to form a perfect square trinomial?

A perfect square is an expression that can be expressed as a square of a real number.

## Answer: The constant value 9 needs to be added to x^{2} - 6x, to make it a perfect square

Let's look into the steps below.

**Explanation:**

Given expression: x^{2}^{ }- 6x

To find the perfect square, we need to add a constant value to this expression, to get the form of (a - b)^{2}.

Let the constant value added be c.

Thus, the expression becomes: x^{2} - 6x + c

We know the algebraic identity, (a - b)^{2} = a^{2 }- 2ab + b^{2}

On comparing x^{2} - 6x + c with a^{2 }- 2ab + b^{2} we get,

a^{2} = x^{2}

Thus, a = x

Also, b^{2} = c and -2ab = -6x

-2xb = -6x [Since, a = x]

Dividing both the sides by -2x, we get,

b = 3

Therefore, c = b^{2} = 3^{2} = 9