%5E2%3D81.jpeg "(x-3)^2=81")
Solving the Equation (x-3)^2 = 81
This equation involves a squared term and can be solved using the following steps:
1. Take the square root of both sides:
Taking the square root of both sides of the equation eliminates the square:
√((x-3)^2) = ±√81
This results in two possible solutions, as the square root of a number can be positive or negative:
x-3 = ±9
2. Solve for x in both cases:
Case 1: x - 3 = 9
Adding 3 to both sides gives:
x = 9 + 3
x = 12
Case 2: x - 3 = -9
Adding 3 to both sides gives:
x = -9 + 3
x = -6
3. Solution
Therefore, the solutions to the equation (x-3)^2 = 81 are x = 12 and x = -6.
Important Note: When solving equations involving squares, it's crucial to remember that taking the square root results in two possible solutions, one positive and one negative.