x+x2+1=(1+x)2

Solution for x+x2+1=(1+x)2 equation:

x+x2+1=(1+x)2

We move all terms to the left:

x+x2+1-((1+x)2)=0

We add all the numbers together, and all the variables

x+x2-((x+1)2)+1=0

We add all the numbers together, and all the variables

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


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

(x+1)2

We multiply parentheses

2x+2

Back to the equation:

-(2x+2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-1x-1=0

a = 1; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·1·(-1)
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{5}}{2*1}=\frac{1-\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{5}}{2*1}=\frac{1+\sqrt{5}}{2}
$