Math Olympiads Problem

>>279772
-Simplify inside parentheses
-Multiply out parentheses
-Move everything to the left, leaving zero on the right
-Simplify left side
-Find roots of quadratic equation

http://m.wikihow.com/Find-the-Roots-of-a-Quadratic-Equation

>>279772
Notice it says
a^2 + b^2 = (a+b)^2,
where
a = (3^x - 27) and
b = (5^x - 625).

Expanding the right side:
a^2 + b^2 = a^2 + 2ab + b^2
Substracting the left hand side:
0 = 2ab
Which is equivalent to a = 0 or b = 0, i.e.
3^x - 27 = 0 or
5^x - 625 = 0.
With real solutions x=3 and x=4 respectively. So the answer is 7.

>>279789
It's not a quadratic equation.