%5E6%3D35.jpeg "(x-2)^6=35")
Solving the Equation (x-2)^6 = 35
This equation involves a sixth power, making it a bit more complex to solve than a simple linear or quadratic equation. Here's a step-by-step guide on how to find the solutions:
1. Isolate the Term with the Variable
To start, we need to isolate the term with the variable, which is (x-2)^6. Since the right side of the equation is already a constant, we are good to go.
2. Take the Sixth Root of Both Sides
To get rid of the sixth power, we take the sixth root of both sides of the equation:
(x-2)^6 = 35
(x-2) = 35^(1/6)
3. Simplify and Solve for x
Now, calculate the sixth root of 35 and simplify the equation:
(x-2) ≈ 1.86
(x) ≈ 1.86 + 2
(x) ≈ 3.86
Understanding the Solutions
It's important to note that when solving equations involving even powers, we often get multiple solutions. In this case, we can also consider the negative sixth root of 35:
(x-2) ≈ -1.86
(x) ≈ -1.86 + 2
(x) ≈ 0.14
Therefore, the equation (x-2)^6 = 35 has two solutions: approximately 3.86 and 0.14.