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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 guide you through solving the equation (x+8)^2 = 25. This equation involves a squared term, and we'll use the concept of square roots to find the solutions.

Understanding the Equation

The equation (x+8)^2 = 25 means that the square of the expression (x+8) is equal to 25.

Solving for x

  1. Take the square root of both sides: To get rid of the square, we take the square root of both sides of the equation:

    √[(x+8)^2] = ±√25

  2. Simplify: The square root of a squared term simply gives us the original term:

    x + 8 = ±5

  3. Isolate x: Subtract 8 from both sides of the equation:

    x = -8 ± 5

  4. Solve for both possibilities: This gives us two possible solutions:

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

Conclusion

Therefore, the solutions to the equation (x+8)^2 = 25 are x = -3 and x = -13.

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