2^18=(2x)^2

Solution for 2^18=(2x)^2 equation:

2^18=(2x)^2

We move all terms to the left:

2^18-((2x)^2)=0

determiningTheFunctionDomain
-2x^2+2^18=0

We add all the numbers together, and all the variables

-2x^2+262144=0

a = -2; b = 0; c = +262144;
Δ = b2-4ac
Δ = 02-4·(-2)·262144
Δ = 2097152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2097152}=\sqrt{1048576*2}=\sqrt{1048576}*\sqrt{2}=1024\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1024\sqrt{2}}{2*-2}=\frac{0-1024\sqrt{2}}{-4}
=-\frac{1024\sqrt{2}}{-4}
=-\frac{256\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1024\sqrt{2}}{2*-2}=\frac{0+1024\sqrt{2}}{-4}
=\frac{1024\sqrt{2}}{-4}
=\frac{256\sqrt{2}}{-1}
$