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(x-4)^2=25 Answer

less than a minute read Jun 17, 2024
(x-4)^2=25 Answer

Solving the Equation: (x - 4)^2 = 25

This equation involves a squared term, which requires a specific approach to solve for x. Here's a breakdown of the steps:

1. Taking the Square Root

  • Isolate the squared term: The equation is already in this form.
  • Take the square root of both sides: This eliminates the square from the left side. Remember that taking the square root results in both positive and negative solutions.
√((x - 4)^2) = ±√25

2. Simplifying the Equation

  • Simplify the square roots: √25 = 5.
  • Solve for x:
x - 4 = ±5

3. Finding the Solutions

  • Positive solution:
x - 4 = 5
x = 5 + 4
x = 9
  • Negative solution:
x - 4 = -5
x = -5 + 4
x = -1

Therefore, the solutions to the equation (x - 4)^2 = 25 are x = 9 and x = -1.

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