16^2x=1/128

Solution for 16^2x=1/128 equation:

16^2x=1/128

We move all terms to the left:

16^2x-(1/128)=0

We add all the numbers together, and all the variables

16^2x-(+1/128)=0

We get rid of parentheses

16^2x-1/128=0

We multiply all the terms by the denominator


16^2x*128-1=0

Wy multiply elements

2048x^2-1=0

a = 2048; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2048·(-1)
Δ = 8192
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:

$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{2}}{2*2048}=\frac{0-64\sqrt{2}}{4096}
=-\frac{64\sqrt{2}}{4096}
=-\frac{\sqrt{2}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{2}}{2*2048}=\frac{0+64\sqrt{2}}{4096}
=\frac{64\sqrt{2}}{4096}
=\frac{\sqrt{2}}{64}
$