<s>[INST] Find x: $2^{2x^2}+2^{x^2+2x+2}=2^{4x+5}$ $$2^{2x^2}+2^{x^2+2x+2}=2^{4x+5}$$
I have to find x in this exponential equation.
I tried to write it in another way, like this:
$2^{2x^2}+2\cdot2^{(x+1)^2}=2\cdot2^{4(x+1)}$
But I don't think this would help.
 [/INST] Divide by $2^{2x^2}$ to get $1 + 2^{-(x-1)^2} \cdot 2^3 = 2^{-2 (x-1)^2} \cdot 2^7$. Substitute $y = 2^{-(x-1)^2}$, and solve the quadratics.
</s>