%5E2%3D64.jpeg "(x-6)^2=64")
Solving the Equation (x-6)^2 = 64
This equation involves a squared term, which means we need to take the square root to solve for x. Here's a step-by-step solution:
1. Take the square root of both sides:
√(x-6)^2 = ±√64
2. Simplify:
x - 6 = ±8
3. Solve for x:
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Case 1: x - 6 = 8 x = 8 + 6 x = 14
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Case 2: x - 6 = -8 x = -8 + 6 x = -2
Therefore, the solutions to the equation (x-6)^2 = 64 are x = 14 and x = -2.
Explanation:
- When we take the square root of both sides, we need to consider both positive and negative values because squaring a positive or negative number results in a positive value.
- The equation represents a quadratic equation, meaning it has two possible solutions.
Verification:
We can check our answers by plugging them back into the original equation:
- For x = 14: (14 - 6)^2 = 8^2 = 64
- For x = -2: (-2 - 6)^2 = (-8)^2 = 64
Both solutions satisfy the original equation.