X2=(1-x)(1+x)

Solution for X2=(1-x)(1+x) equation:

X2=(1-X)(1+X)

We move all terms to the left:

X2-((1-X)(1+X))=0

We add all the numbers together, and all the variables

X2-((-1X+1)(X+1))=0

We add all the numbers together, and all the variables

X^2-((-1X+1)(X+1))=0

We multiply parentheses ..

X^2-((-1X^2-1X+X+1))=0


We calculate terms in parentheses: -((-1X^2-1X+X+1)), so:

(-1X^2-1X+X+1)

We get rid of parentheses

-1X^2-1X+X+1

We add all the numbers together, and all the variables

-1X^2+1

Back to the equation:

-(-1X^2+1)


We get rid of parentheses

X^2+1X^2-1=0

We add all the numbers together, and all the variables

2X^2-1=0

a = 2; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2·(-1)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*2}=\frac{0-2\sqrt{2}}{4}
=-\frac{2\sqrt{2}}{4}
=-\frac{\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*2}=\frac{0+2\sqrt{2}}{4}
=\frac{2\sqrt{2}}{4}
=\frac{\sqrt{2}}{2}
$