4 log 2 x + x^2 = 8 we can write
(2^2)^(log2 x) + x^2 = 8
2^(2 log 2x) + x^2 = 8
2^( log 2 x^2) + x^2 = 8
[ Note that we have the property that a ^ (log a b^2) = b^2 ]
x^2 + x^2 = 8
2x^2 = 8 divide both sides by 2
x^2 = 4 take the positive root
x = 2