2^-x^2=0.25

Solution for 2^-x^2=0.25 equation:

2^-x^2=0.25

We move all terms to the left:

2^-x^2-(0.25)=0

We add all the numbers together, and all the variables

-1x^2+0.84089641525371=0

a = -1; b = 0; c = +0.84089641525371;
Δ = b2-4ac
Δ = 02-4·(-1)·0.84089641525371
Δ = 3.3635856610148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{3.3635856610148}}{2*-1}=\frac{0-\sqrt{3.3635856610148}}{-2}
=-\frac{\sqrt{}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{3.3635856610148}}{2*-1}=\frac{0+\sqrt{3.3635856610148}}{-2}
=\frac{\sqrt{}}{-2}
$