X2+y2=125

Solution for X2+y2=125 equation:

X2+X2=125

We move all terms to the left:

X2+X2-(125)=0

We add all the numbers together, and all the variables

2X^2-125=0

a = 2; b = 0; c = -125;
Δ = b2-4ac
Δ = 02-4·2·(-125)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{10}}{2*2}=\frac{0-10\sqrt{10}}{4}
=-\frac{10\sqrt{10}}{4}
=-\frac{5\sqrt{10}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{10}}{2*2}=\frac{0+10\sqrt{10}}{4}
=\frac{10\sqrt{10}}{4}
=\frac{5\sqrt{10}}{2}
$