%5E2%3D7.jpeg "(x-1)^2=7")
Solving the Equation (x-1)^2 = 7
This equation involves a squared term, which means we'll need to use the square root property to solve for x. Here's how to break down the steps:
1. Isolate the Squared Term
The squared term is already isolated on the left side of the equation:
(x - 1)^2 = 7
2. Apply the Square Root Property
Taking the square root of both sides of the equation, we get:
√[(x - 1)^2] = ±√7
Remember that we need to consider both the positive and negative square roots of 7.
3. Simplify and Solve for x
The square root cancels out the square on the left side:
x - 1 = ±√7
Now, isolate x by adding 1 to both sides:
x = 1 ± √7
4. Express the Solutions
This gives us two possible solutions for x:
- x = 1 + √7
- x = 1 - √7
These are the exact solutions to the equation (x - 1)^2 = 7.
Conclusion
By using the square root property and careful simplification, we have successfully solved the equation (x - 1)^2 = 7, obtaining two distinct solutions: x = 1 + √7 and x = 1 - √7.