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Solving the Equation (x+2)² = 64
This equation involves a squared term, making it a quadratic equation. Let's break down the steps to solve it:
1. Take the Square Root of Both Sides
The first step is to isolate the term inside the parentheses. We can do this by taking the square root of both sides of the equation:
√((x+2)²) = ±√64
This simplifies to:
x + 2 = ±8
2. Solve for x
Now, we have two possible solutions:
Case 1: x + 2 = 8
Subtracting 2 from both sides gives:
x = 6
Case 2: x + 2 = -8
Subtracting 2 from both sides gives:
x = -10
3. The Solutions
Therefore, the solutions to the equation (x+2)² = 64 are x = 6 and x = -10.
Verification
To verify our solutions, we can substitute them back into the original equation:
- For x = 6: (6 + 2)² = 8² = 64
- For x = -10: (-10 + 2)² = (-8)² = 64
Both solutions satisfy the original equation.