X2+y2=106

Solution for X2+y2=106 equation:

X2+X2=106

We move all terms to the left:

X2+X2-(106)=0

We add all the numbers together, and all the variables

2X^2-106=0

a = 2; b = 0; c = -106;
Δ = b2-4ac
Δ = 02-4·2·(-106)
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{53}}{2*2}=\frac{0-4\sqrt{53}}{4}
=-\frac{4\sqrt{53}}{4}
=-\sqrt{53}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{53}}{2*2}=\frac{0+4\sqrt{53}}{4}
=\frac{4\sqrt{53}}{4}
=\sqrt{53}
$