%5E2%3D36.jpeg "(x-5)^2=36")
Solving the Equation: (x - 5)^2 = 36
This equation presents a simple quadratic equation in disguise. Let's break down how to solve it:
Understanding the Equation
The equation (x - 5)^2 = 36 represents the square of a binomial. To solve for x, we need to isolate it.
Solving for x
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Take the square root of both sides: √((x - 5)^2) = ±√36
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Simplify: x - 5 = ±6
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Isolate x: x = 5 ± 6
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Calculate the two possible solutions:
- x = 5 + 6 = 11
- x = 5 - 6 = -1
The Solutions
Therefore, the solutions to the equation (x - 5)^2 = 36 are x = 11 and x = -1.
Verification
We can verify our solutions by plugging them back into the original equation:
- For x = 11: (11 - 5)^2 = 6^2 = 36
- For x = -1: (-1 - 5)^2 = (-6)^2 = 36
Both solutions satisfy the original equation, confirming their validity.
Conclusion
This example demonstrates how to solve a quadratic equation presented in a slightly different form. By utilizing basic algebraic operations and understanding the concept of square roots, we can arrive at the correct solutions.