What constant can be added to x² - 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: 9 needs to be added to x² - 6x to make it a perfect square.

Let's look into the steps below.

Explanation:

Given expression: x² - 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: x² - 6x + c

We know the algebraic identity, (a - b)² = a² - 2ab + b²

On comparing x² - 6x + c with a² - 2ab + b² we get,

a² = x² 

Thus, a = x

Also, b² = c and -2ab = -6x

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

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

b = 3

Therefore, c = b² = 3² = 9.

Thus, 9 needs to be added to x² - 6x to make it a perfect square.