%5E2%3D121.jpeg "(x-5)^2=121")
Solving the Equation: (x-5)^2 = 121
This equation involves a squared term, and our goal is to find the values of 'x' that satisfy the equation. Let's break down the steps:
1. Taking the Square Root
First, we need to isolate the term inside the parentheses. To do this, we take the square root of both sides of the equation:
√[(x-5)^2] = ±√121
This gives us:
x - 5 = ±11
2. Solving for x
Now, we have two possible solutions:
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Case 1: x - 5 = 11 Adding 5 to both sides, we get: x = 16
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Case 2: x - 5 = -11 Adding 5 to both sides, we get: x = -6
3. The Solutions
Therefore, the solutions to the equation (x-5)^2 = 121 are x = 16 and x = -6.
These solutions represent the two values of 'x' that, when plugged into the original equation, will result in a true statement.