(x-1)^2=7

2 min read Jun 17, 2024
(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.

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