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Solving the Equation (x+2)² = 64
This article will guide you through solving the equation (x+2)² = 64. This equation involves a squared term, which requires us to use the concept of square roots to find the solution.
Understanding the Equation
The equation (x+2)² = 64 represents a quadratic equation. Here's a breakdown:
- (x+2)²: This represents the square of the expression (x+2).
- 64: This is a constant value.
To solve for 'x', we need to isolate it.
Solving for 'x'
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Take the square root of both sides: √(x+2)² = ±√64
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Simplify: x + 2 = ±8
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Isolate 'x': x = -2 ± 8
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Find the two possible solutions:
- x = -2 + 8 = 6
- x = -2 - 8 = -10
Verification
We can verify our solutions by plugging them back into the original equation:
- For x = 6: (6+2)² = 8² = 64 (This is true)
- For x = -10: (-10+2)² = (-8)² = 64 (This is also true)
Conclusion
Therefore, the solutions to the equation (x+2)² = 64 are x = 6 and x = -10. This method demonstrates how to solve quadratic equations by utilizing the concept of square roots.