(x-1)^2-19=81

2 min read Jun 17, 2024
(x-1)^2-19=81

Solving the Equation: (x - 1)^2 - 19 = 81

This article will guide you through the steps to solve the equation (x - 1)^2 - 19 = 81. Let's break it down!

1. Isolate the Squared Term

Our goal is to get the term with the variable (x - 1)^2 by itself. To do this, we'll add 19 to both sides of the equation:

(x - 1)^2 - 19 + 19 = 81 + 19

This simplifies to:

(x - 1)^2 = 100

2. Take the Square Root

Now, to get rid of the square, we take the square root of both sides of the equation:

√(x - 1)^2 = ±√100

Remember that when taking the square root, we need to consider both the positive and negative solutions. This gives us:

(x - 1) = ±10

3. Solve for x

We now have two separate equations to solve:

  • x - 1 = 10
  • x - 1 = -10

Solving for x in the first equation: x - 1 + 1 = 10 + 1 x = 11

Solving for x in the second equation: x - 1 + 1 = -10 + 1 x = -9

Conclusion

Therefore, the solutions to the equation (x - 1)^2 - 19 = 81 are x = 11 and x = -9.

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