2^(2x)=1/64

Solution for 2^(2x)=1/64 equation:

2^(2x)=1/64

We move all terms to the left:

2^(2x)-(1/64)=0

We add all the numbers together, and all the variables

2^2x-(+1/64)=0

We get rid of parentheses

2^2x-1/64=0

We multiply all the terms by the denominator


2^2x*64-1=0

Wy multiply elements

128x^2-1=0

a = 128; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·128·(-1)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{2}}{2*128}=\frac{0-16\sqrt{2}}{256}
=-\frac{16\sqrt{2}}{256}
=-\frac{\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{2}}{2*128}=\frac{0+16\sqrt{2}}{256}
=\frac{16\sqrt{2}}{256}
=\frac{\sqrt{2}}{16}
$