x^2+2x+1+x^2=841

Solution for x^2+2x+1+x^2=841 equation:

x^2+2x+1+x^2=841

We move all terms to the left:

x^2+2x+1+x^2-(841)=0

We add all the numbers together, and all the variables

2x^2+2x-840=0

a = 2; b = 2; c = -840;
Δ = b2-4ac
Δ = 22-4·2·(-840)
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-82}{2*2}=\frac{-84}{4}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+82}{2*2}=\frac{80}{4}
=20
$