Solving the Equation (x + 7)² = 81
This article will guide you through solving the equation (x + 7)² = 81. We will use the principles of square roots and algebraic manipulation to find the values of x that satisfy this equation.
Understanding the Equation
The equation involves a squared term, (x + 7)², which represents the square of the expression (x + 7). The equation states that this square is equal to 81. To find the possible values of x, we need to isolate x by taking the square root of both sides.
Solving for x

Take the square root of both sides:
√[(x + 7)²] = ±√81

Simplify:
x + 7 = ±9

Isolate x:
x = 7 ± 9

Solve for the two possible values of x:
 x = 7 + 9 = 2
 x = 7  9 = 16
Solution
Therefore, the solutions to the equation (x + 7)² = 81 are x = 2 and x = 16.
Verification
We can verify these solutions by substituting them back into the original equation:
 For x = 2: (2 + 7)² = 9² = 81 (True)
 For x = 16: (16 + 7)² = (9)² = 81 (True)
Both solutions satisfy the original equation, confirming our results.