X^2+y^2=725

Solution for X^2+y^2=725 equation:

X^2+X^2=725

We move all terms to the left:

X^2+X^2-(725)=0

We add all the numbers together, and all the variables

2X^2-725=0

a = 2; b = 0; c = -725;
Δ = b2-4ac
Δ = 02-4·2·(-725)
Δ = 5800
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:

$\sqrt{\Delta}=\sqrt{5800}=\sqrt{100*58}=\sqrt{100}*\sqrt{58}=10\sqrt{58}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{58}}{2*2}=\frac{0-10\sqrt{58}}{4}
=-\frac{10\sqrt{58}}{4}
=-\frac{5\sqrt{58}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{58}}{2*2}=\frac{0+10\sqrt{58}}{4}
=\frac{10\sqrt{58}}{4}
=\frac{5\sqrt{58}}{2}
$