2^1-x^2=1/256

Solution for 2^1-x^2=1/256 equation:

2^1-x^2=1/256

We move all terms to the left:

2^1-x^2-(1/256)=0

We add all the numbers together, and all the variables

-x^2+2^1-(+1/256)=0

We add all the numbers together, and all the variables

-1x^2+2-(+1/256)=0

We get rid of parentheses

-1x^2+2-1/256=0

We multiply all the terms by the denominator


-1x^2*256-1+2*256=0

We add all the numbers together, and all the variables

-1x^2*256+511=0

Wy multiply elements

-256x^2+511=0

a = -256; b = 0; c = +511;
Δ = b2-4ac
Δ = 02-4·(-256)·511
Δ = 523264
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:

$\sqrt{\Delta}=\sqrt{523264}=\sqrt{1024*511}=\sqrt{1024}*\sqrt{511}=32\sqrt{511}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{511}}{2*-256}=\frac{0-32\sqrt{511}}{-512}
=-\frac{32\sqrt{511}}{-512}
=-\frac{\sqrt{511}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{511}}{2*-256}=\frac{0+32\sqrt{511}}{-512}
=\frac{32\sqrt{511}}{-512}
=\frac{\sqrt{511}}{-16}
$