Solving the Equation (x-6)^2 = 9
This article will guide you through solving the equation (x-6)^2 = 9. We will explore the steps involved in finding the solutions for x.
Understanding the Equation
The equation (x-6)^2 = 9 represents a quadratic equation. It involves a squared term, which means we have two possible solutions for x.
Solving the Equation
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Take the square root of both sides: To get rid of the square, we take the square root of both sides of the equation. Remember that taking the square root introduces both positive and negative solutions.
√(x-6)^2 = ±√9
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Simplify: Simplifying both sides gives us:
x - 6 = ±3
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Isolate x: To find the values of x, we add 6 to both sides of the equation:
x = 6 ± 3
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Calculate the solutions: This gives us two solutions:
- x = 6 + 3 = 9
- x = 6 - 3 = 3
Verifying the Solutions
We can verify our solutions by substituting them back into the original equation:
- For x = 9: (9 - 6)^2 = 3^2 = 9
- For x = 3: (3 - 6)^2 = (-3)^2 = 9
Both solutions satisfy the original equation.
Conclusion
The solutions for the equation (x-6)^2 = 9 are x = 9 and x = 3. This demonstrates the process of solving quadratic equations with squared terms. By taking the square root of both sides and isolating x, we can find the two possible solutions.