%5E2%3D49.jpeg "(x-9)^2=49")
Solving the Equation (x-9)² = 49
This article will guide you through solving the equation (x-9)² = 49.
Understanding the Equation
The equation involves a squared term, which means we need to consider both positive and negative solutions.
Solving for x
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Take the square root of both sides: √((x-9)²) = ±√49
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Simplify: x - 9 = ±7
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Isolate x: x = 9 ± 7
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Calculate both possible solutions:
- x = 9 + 7 = 16
- x = 9 - 7 = 2
Solutions
Therefore, the solutions to the equation (x-9)² = 49 are x = 16 and x = 2.
Verification
We can verify our solutions by plugging them back into the original equation:
- For x = 16: (16-9)² = 7² = 49 (correct)
- For x = 2: (2-9)² = (-7)² = 49 (correct)
Both solutions satisfy the original equation.