Jasonbradley
Home

(x-1)^2=25 Square Root Method

2 min read Jun 17, 2024
(x-1)^2=25 Square Root Method

Solving Equations Using the Square Root Method: (x-1)^2 = 25

The square root method is a useful technique for solving equations that involve a squared term. Let's look at how to solve the equation (x-1)^2 = 25 using this method.

Steps to Solve Using the Square Root Method

  1. Isolate the squared term: In this case, the squared term is already isolated on the left side of the equation.

  2. Take the square root of both sides: Remember that when you take the square root of a number, there are both positive and negative solutions.

    √[(x-1)²] = ±√25

  3. Simplify: The square root of (x-1)² is simply (x-1), and the square root of 25 is 5. This gives us:

    x-1 = ±5

  4. Solve for x: To isolate x, we need to add 1 to both sides of the equation.

    x = 1 ± 5

  5. Find the two solutions:

    • x = 1 + 5 = 6
    • x = 1 - 5 = -4

Therefore, the solutions to the equation (x-1)^2 = 25 are x = 6 and x = -4.

Key Points to Remember

  • When using the square root method, remember to consider both the positive and negative square roots.
  • This method is particularly effective for equations where the squared term is already isolated.

By following these steps, you can successfully solve equations using the square root method and find the solutions for any quadratic equation that can be simplified into this form.

Related Post

Featured Posts