(x-8)2=36

2 min read Jun 17, 2024

Solving the Equation: (x - 8)² = 36

This article will guide you through solving the equation (x - 8)² = 36.

Understanding the Equation

The equation presents a quadratic expression, meaning it involves a variable raised to the power of 2. To solve for x, we need to isolate it.

Steps to Solve

Take the square root of both sides:
- √((x - 8)²) = ±√36
- (x - 8) = ±6
Solve for x:
- Case 1: (x - 8) = 6
  - x = 6 + 8
  - x = 14
- Case 2: (x - 8) = -6
  - x = -6 + 8
  - x = 2

Solution

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

Verification

We can verify our solutions by plugging them back into the original equation:

For x = 14: (14 - 8)² = 6² = 36 (True)
For x = 2: (2 - 8)² = (-6)² = 36 (True)

Conclusion

We successfully solved the equation (x - 8)² = 36 by using the square root property and finding two distinct solutions for x. It's essential to remember that taking the square root of a number yields both positive and negative results, which is why we considered both cases in our solution.