# What number should be added to both sides of the equation to complete the square x^{2} – 6x = 5?

Quadratic equations are second-degree algebraic expressions and are of the form ax^{2} + bx + c = 0.

### Answer: 9 should be added to both sides of the equation to complete the square x^{2} – 6x = 5.

Let's look into the steps explained below

**Explanation:**

Given: A quadratic equation x^{2} – 6x = 5

Let's express x^{2} – 6x = 5 in standard form.

Thus, we have x^{2} - 6x - 5 = 0

We will be using completing the square method to solve the given question.

x^{2} - 6x - 5 = 0

⇒ x^{2} - 2 × 3x - 5 = 0

⇒ x^{2} - 2 × 3x - 5 + 3^{2} - 3^{2} = 0 [ Adding and subtracting 3^{2} in the equation]

⇒ (x^{2} - 2 × 3x + 3^{2} ) - 3^{2} - 5 = 0

⇒ (x^{2} - 2 × 3x + 9 ) = 5 + 9 -------------- (1)

⇒ (x - 3)^{2} = 5 + 9 [ Using the algebraic identity (a - b)^{2} = a^{2} - 2ab + b^{2} ]

From (1) we see that 9 is to be added on both the sides of the equation.

Thus, the given equation x^{2} - 6x = 5 is now converted to (x - 3)^{2} = 5 + 9 using completing the whole square method.