(x-2)^2=28

2 min read Jun 17, 2024
(x-2)^2=28

Solving the Equation (x-2)^2 = 28

This article will guide you through the steps of solving the equation (x-2)^2 = 28.

Understanding the Equation

The equation (x-2)^2 = 28 is a quadratic equation in disguise. Let's break it down:

  • (x-2)^2 represents the square of the expression (x-2). This means we are multiplying (x-2) by itself.
  • 28 is the constant term on the right-hand side of the equation.

Solving for x

To solve for x, we need to isolate it. Here's how:

  1. Take the square root of both sides:

    √[(x-2)^2] = ±√28

  2. Simplify:

    x - 2 = ±√28

    Note: Remember that taking the square root of a number results in both a positive and a negative solution.

  3. Simplify the radical:

    x - 2 = ±2√7

  4. Isolate x:

    x = 2 ± 2√7

The Solutions

Therefore, the solutions to the equation (x-2)^2 = 28 are:

  • x = 2 + 2√7
  • x = 2 - 2√7

Conclusion

By applying the steps of taking the square root and simplifying, we successfully solved the equation (x-2)^2 = 28. The solutions are x = 2 + 2√7 and x = 2 - 2√7.