x2+(x+2)2=100

Solution for x2+(x+2)2=100 equation:

x2+(x+2)2=100

We move all terms to the left:

x2+(x+2)2-(100)=0

We add all the numbers together, and all the variables

x^2+(x+2)2-100=0

We multiply parentheses

x^2+2x+4-100=0

We add all the numbers together, and all the variables

x^2+2x-96=0

a = 1; b = 2; c = -96;
Δ = b2-4ac
Δ = 22-4·1·(-96)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{97}}{2*1}=\frac{-2-2\sqrt{97}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{97}}{2*1}=\frac{-2+2\sqrt{97}}{2}
$