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(x-5)^2-100=0

2 min read Jun 17, 2024
(x-5)^2-100=0

Solving the Quadratic Equation: (x-5)^2 - 100 = 0

This article will guide you through solving the quadratic equation (x-5)^2 - 100 = 0. We will use a combination of algebraic manipulation and the square root property to find the solutions.

Understanding the Equation

The given equation is a quadratic equation because it has a term with the highest power of x as 2. The equation is in a slightly disguised form. Let's break it down:

  • (x-5)^2: This represents the square of the expression (x-5).
  • -100: This is a constant term.

Solving the Equation

  1. Isolate the squared term: Begin by adding 100 to both sides of the equation: (x-5)^2 = 100

  2. Apply the square root property: Take the square root of both sides of the equation. Remember that taking the square root introduces both positive and negative solutions: x - 5 = ±√100

  3. Simplify: √100 = 10, so we have: x - 5 = ±10

  4. Solve for x: Add 5 to both sides of the equation: x = 5 ± 10

  5. Find the two solutions:

    • x = 5 + 10 = 15
    • x = 5 - 10 = -5

Conclusion

Therefore, the solutions to the quadratic equation (x-5)^2 - 100 = 0 are x = 15 and x = -5.

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