Solving the Equation: (x  5)^2 = 36
This equation presents a simple quadratic equation in disguise. Let's break down how to solve it:
Understanding the Equation
The equation (x  5)^2 = 36 represents the square of a binomial. To solve for x, we need to isolate it.
Solving for x

Take the square root of both sides: √((x  5)^2) = ±√36

Simplify: x  5 = ±6

Isolate x: x = 5 ± 6

Calculate the two possible solutions:
 x = 5 + 6 = 11
 x = 5  6 = 1
The Solutions
Therefore, the solutions to the equation (x  5)^2 = 36 are x = 11 and x = 1.
Verification
We can verify our solutions by plugging them back into the original equation:
 For x = 11: (11  5)^2 = 6^2 = 36
 For x = 1: (1  5)^2 = (6)^2 = 36
Both solutions satisfy the original equation, confirming their validity.
Conclusion
This example demonstrates how to solve a quadratic equation presented in a slightly different form. By utilizing basic algebraic operations and understanding the concept of square roots, we can arrive at the correct solutions.