x2+(x+1)2=221

Solution for x2+(x+1)2=221 equation:

x2+(x+1)2=221

We move all terms to the left:

x2+(x+1)2-(221)=0

We add all the numbers together, and all the variables

x^2+(x+1)2-221=0

We multiply parentheses

x^2+2x+2-221=0

We add all the numbers together, and all the variables

x^2+2x-219=0

a = 1; b = 2; c = -219;
Δ = b2-4ac
Δ = 22-4·1·(-219)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{55}}{2*1}=\frac{-2-4\sqrt{55}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{55}}{2*1}=\frac{-2+4\sqrt{55}}{2}
$