# What number should be added to both sides of the equation to complete the square (x² – 6x = 5)?

Updated on January 19, 2024

Answer: The number 9 should be added to both sides to complete the square.

## Completing the Square

Completing the square is a technique used in algebra to solve quadratic equations. The method involves converting the quadratic equation into a perfect square trinomial by adding a specific value to both sides. For the equation x² – 6x = 5, we take half of the coefficient of x, which is -6/2 = -3, and square it, giving us 9. Adding 9 to both sides gives us x² – 6x + 9 = 14, which can be written as (x – 3)² = 14. This method is not just a mathematical trick; it’s a fundamental concept that helps in understanding the nature of quadratic equations and is widely used in various branches of mathematics, physics, and engineering.

## FAQ on Completing the Square

### How do you solve a quadratic equation by factoring?

Set the equation to zero, find factors of the quadratic, and solve for the variable.

### What is the quadratic formula?

The quadratic formula is x = (-b ± √(b² – 4ac)) / (2a).

### What is the discriminant in a quadratic equation?

The discriminant is b² – 4ac and determines the nature of the roots.