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Solving the Equation (x-2)^2 = 49
This article will guide you through the steps of solving the equation (x-2)^2 = 49.
Understanding the Equation
The equation involves a squared term, indicating a quadratic equation. To solve for 'x', we need to isolate it.
Step 1: Taking the Square Root
To get rid of the square, we take the square root of both sides of the equation:
√((x-2)²) = ±√49
This leads to two possible solutions:
- x - 2 = 7
- x - 2 = -7
Step 2: Isolating 'x'
Now, we need to isolate 'x' in both equations:
- For x - 2 = 7, add 2 to both sides: x = 9
- For x - 2 = -7, add 2 to both sides: x = -5
Solutions
Therefore, the solutions to the equation (x-2)² = 49 are x = 9 and x = -5.
Verification
We can verify our solutions by plugging them back into the original equation:
- For x = 9: (9-2)² = 7² = 49
- For x = -5: (-5-2)² = (-7)² = 49
Both solutions satisfy the original equation.