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Solving the Equation (x-9)^2 = 81
This article will guide you through solving the equation (x-9)^2 = 81. We will explore the steps involved in finding the solutions for x.
Understanding the Equation
The equation (x-9)^2 = 81 represents a quadratic equation. It is in a squared form, meaning we need to find the values of x that, when plugged into the equation, make the left side equal to 81.
Solving for x
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Take the square root of both sides:
- √(x-9)^2 = ±√81
- x - 9 = ±9
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Isolate x:
- x = 9 ± 9
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Solve for both possible values of x:
- x = 9 + 9 = 18
- x = 9 - 9 = 0
Therefore, the solutions to the equation (x-9)^2 = 81 are x = 18 and x = 0.
Verification
To verify our solutions, we can substitute them back into the original equation:
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For x = 18:
- (18 - 9)^2 = 9^2 = 81 (Correct)
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For x = 0:
- (0 - 9)^2 = (-9)^2 = 81 (Correct)
Conclusion
We have successfully solved the quadratic equation (x-9)^2 = 81 and found its solutions to be x = 18 and x = 0. By taking the square root of both sides and isolating x, we were able to determine the values that satisfy the equation.