(x-6)^2=25

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-6)^2 = 25

This article will guide you through solving the equation (x-6)^2 = 25. We will explore two methods to find the solutions for x.

Method 1: Using the Square Root Property

1. Take the square root of both sides: √((x-6)^2) = ±√25

2. Simplify: x - 6 = ±5

3. Isolate x: x = 6 ± 5

4. Solve for both possible values:

   • x = 6 + 5 = 11
   • x = 6 - 5 = 1

Therefore, the solutions to the equation (x-6)^2 = 25 are x = 11 and x = 1.

Method 2: Expanding and Solving the Quadratic Equation

1. Expand the left side of the equation: (x - 6)(x - 6) = 25 x^2 - 12x + 36 = 25

2. Move all terms to one side: x^2 - 12x + 11 = 0

3. Factor the quadratic equation: (x - 1)(x - 11) = 0

4. Set each factor equal to zero and solve for x:

   • x - 1 = 0 => x = 1
   • x - 11 = 0 => x = 11

As you can see, both methods lead to the same solutions: x = 1 and x = 11.

Key Takeaway: Understanding both methods will provide you with a comprehensive approach to solving equations of this type. The choice of method depends on your preference and the complexity of the equation.