%5E2%2B(x-8)%5E2%3D2x%5E2.jpeg "(x-2)^2+(x-8)^2=2x^2")
Solving the Equation (x-2)^2 + (x-8)^2 = 2x^2
This equation involves squaring terms and can be solved using algebraic manipulations. Let's break down the steps to find the solution:
1. Expand the Squares
First, expand the squared terms on the left side of the equation:
- (x-2)^2 = x^2 - 4x + 4
- (x-8)^2 = x^2 - 16x + 64
Substituting these back into the original equation gives:
(x^2 - 4x + 4) + (x^2 - 16x + 64) = 2x^2
2. Simplify the Equation
Combine like terms on the left side:
2x^2 - 20x + 68 = 2x^2
Now, subtract 2x^2 from both sides:
-20x + 68 = 0
3. Solve for x
Isolate the x term by subtracting 68 from both sides:
-20x = -68
Finally, divide both sides by -20 to find the solution:
x = -68 / -20 = 3.4
Therefore, the solution to the equation (x-2)^2 + (x-8)^2 = 2x^2 is x = 3.4.