(x-8)^2-36=0

2 min read Jun 17, 2024

Solving the Equation: (x - 8)^2 - 36 = 0

This article will guide you through the steps of solving the quadratic equation (x - 8)^2 - 36 = 0.

Understanding the Equation

The equation (x - 8)^2 - 36 = 0 is a quadratic equation in standard form. This form is often written as ax^2 + bx + c = 0, where a, b, and c are constants. In our equation, a = 1, b = -16, and c = -28.

Steps to Solve the Equation

Isolate the squared term:
- Add 36 to both sides of the equation: (x - 8)^2 = 36
Take the square root of both sides:
- Remember to consider both positive and negative roots: x - 8 = ±6
Solve for x:
- Case 1: x - 8 = 6
  - Add 8 to both sides: x = 14
- Case 2: x - 8 = -6
  - Add 8 to both sides: x = 2

Solutions

Therefore, the solutions to the equation (x - 8)^2 - 36 = 0 are x = 14 and x = 2.

Verification

You can always verify your solutions by plugging them back into the original equation. Let's check:

For x = 14:
- (14 - 8)^2 - 36 = 6^2 - 36 = 36 - 36 = 0
For x = 2:
- (2 - 8)^2 - 36 = (-6)^2 - 36 = 36 - 36 = 0

As you can see, both solutions satisfy the equation.