%5E2-13%3D68.jpeg "(x-9)^2-13=68")
Solving the Equation: (x-9)^2 - 13 = 68
This article will guide you through the steps of solving the equation (x-9)^2 - 13 = 68.
1. Isolate the Squared Term
First, we need to isolate the term with the squared variable. To do this, we will add 13 to both sides of the equation:
(x-9)^2 - 13 + 13 = 68 + 13
This simplifies to:
(x-9)^2 = 81
2. Take the Square Root
Now, to get rid of the square, we take the square root of both sides of the equation. Remember that taking the square root results in both a positive and negative solution:
√(x-9)^2 = ±√81
This simplifies to:
x - 9 = ±9
3. Solve for x
Finally, we solve for x by adding 9 to both sides of the equation. This results in two possible solutions:
x = 9 + 9 or x = 9 - 9
Therefore, the solutions to the equation (x-9)^2 - 13 = 68 are:
x = 18 and x = 0.
Conclusion
By following these simple steps, we were able to solve the equation (x-9)^2 - 13 = 68 and find its two possible solutions: x = 18 and x = 0. Remember to always check your answers by substituting them back into the original equation to ensure they are valid.