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(x-8)^2=25

2 min read Jun 17, 2024
(x-8)^2=25

Solving the Equation (x-8)^2 = 25

This article will walk you through the steps to solve the equation (x-8)^2 = 25.

Understanding the Equation

The equation involves a squared term, which means we need to consider both positive and negative solutions. Here's how to break it down:

  1. Square Root Property: To get rid of the square, we take the square root of both sides of the equation. Remember, the square root of a number can be both positive and negative. This gives us: √[(x-8)^2] = ±√25

  2. Simplifying: Simplifying the square root on both sides results in: x - 8 = ±5

  3. Solving for x: Now, we need to isolate x. We can do this by adding 8 to both sides of the equation: x = 8 ± 5

  4. Two Solutions: This gives us two possible solutions:

    • x = 8 + 5 = 13
    • x = 8 - 5 = 3

Checking the Solutions

To ensure our solutions are correct, we can plug them back into the original equation:

  • For x = 13: (13 - 8)^2 = 5^2 = 25. This solution works.
  • For x = 3: (3 - 8)^2 = (-5)^2 = 25. This solution also works.

Conclusion

Therefore, the solutions to the equation (x-8)^2 = 25 are x = 13 and x = 3. Remember, always check your solutions by plugging them back into the original equation to ensure accuracy.

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