(х-6)^2+(х+8)^2=2х^2

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To solve this equation, we first need to expand both sides:

(x-6)^2 = x^2 - 12x + 36
(x+8)^2 = x^2 + 16x + 64

Now we can rewrite the equation:

x^2 - 12x + 36 + x^2 + 16x + 64 = 2x^2

Combining like terms:

2x^2 + 4x + 100 = 2x^2

Next, we can subtract 2x^2 from both sides to simplify the equation:

4x + 100 = 0

Now we can solve for x:

4x = -100
x = -25

Therefore, the solution to the equation is x = -25.