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Solving the Equation (x+15)² = 81
This article will guide you through the process of solving the equation (x+15)² = 81. We will use the properties of square roots and basic algebraic manipulation to find the solution(s).
Understanding the Equation
The equation represents a quadratic equation in the form of (x + a)² = b, where 'a' and 'b' are constants. To solve for 'x', we need to isolate it by undoing the operations performed on it.
Solving for x
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Take the square root of both sides:
Since the left side of the equation is squared, we can eliminate the square by taking the square root of both sides: √[(x+15)²] = ±√81 -
Simplify: The square root of (x+15)² is (x+15), and the square root of 81 is 9. Remember that taking the square root results in both positive and negative values. x + 15 = ±9
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Solve for x: We now have two separate equations:
- x + 15 = 9
- x + 15 = -9
Solving for 'x' in each equation:
- x = 9 - 15 = -6
- x = -9 - 15 = -24
Solution
Therefore, the solutions to the equation (x+15)² = 81 are x = -6 and x = -24.
Verification
We can verify our solutions by substituting them back into the original equation:
- For x = -6: (-6 + 15)² = 9² = 81 (True)
- For x = -24: (-24 + 15)² = (-9)² = 81 (True)
This confirms that both solutions are valid.