2^2x=4/64

Solution for 2^2x=4/64 equation:

2^2x=4/64

We move all terms to the left:

2^2x-(4/64)=0

We add all the numbers together, and all the variables

2^2x-(+4/64)=0

We get rid of parentheses

2^2x-4/64=0

We multiply all the terms by the denominator


2^2x*64-4=0

Wy multiply elements

128x^2-4=0

a = 128; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·128·(-4)
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{2}}{2*128}=\frac{0-32\sqrt{2}}{256}
=-\frac{32\sqrt{2}}{256}
=-\frac{\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{2}}{2*128}=\frac{0+32\sqrt{2}}{256}
=\frac{32\sqrt{2}}{256}
=\frac{\sqrt{2}}{8}
$