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

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

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.