%5E2%3D81.jpeg "(x-1)^2=81")
Solving the Equation: (x-1)^2 = 81
This equation presents a simple quadratic equation that we can solve using basic algebraic techniques. Let's break down the steps:
1. Taking the Square Root of Both Sides
Since we have a squared term on the left side, our first step is to get rid of that by taking the square root of both sides:
√[(x-1)^2] = ±√81
Remember that when taking the square root of a number, we need to consider both positive and negative solutions.
2. Simplifying
Simplifying both sides gives us:
x - 1 = ±9
3. Isolating x
To isolate x, we need to add 1 to both sides:
x = 1 ± 9
4. Solving for Both Possibilities
This gives us two possible solutions:
- x = 1 + 9 = 10
- x = 1 - 9 = -8
Conclusion
Therefore, the solutions to the equation (x-1)^2 = 81 are x = 10 and x = -8.