Question 417717
Square both sides of the equation:

{{{x+7 = x^2 -10x + 25}}}
{{{0 = x^2 - 11x + 18}}}
0 = (x - 2)(x - 9) ==> x = 2, 9.

x = 2 doesn't satisfy the original equation, while x = 9 does.
Therefore the final answer is x = 9.