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Solving the Equation (x-4)^2 = 169
This article will guide you through the steps to solve the equation (x-4)^2 = 169.
Understanding the Equation
The equation (x-4)^2 = 169 is a quadratic equation. It involves a squared term (x-4)^2. To solve for x, we need to isolate it.
Steps to Solve
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Take the square root of both sides:
√((x-4)^2) = ±√169
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Simplify:
x-4 = ±13
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Solve for x:
x = 4 ± 13
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Calculate the two possible solutions:
x = 4 + 13 = 17 x = 4 - 13 = -9
The Solutions
Therefore, the solutions to the equation (x-4)^2 = 169 are x = 17 and x = -9.
Verification
We can verify our solutions by plugging them back into the original equation:
- For x = 17: (17 - 4)^2 = 13^2 = 169
- For x = -9: (-9 - 4)^2 = (-13)^2 = 169
Both solutions satisfy the original equation.
Conclusion
By following the steps outlined above, we have successfully solved the equation (x-4)^2 = 169. The solutions are x = 17 and x = -9. Remember that when taking the square root of both sides of an equation, we must consider both the positive and negative roots.