%5E2-19%3D81.jpeg "(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.