X2+y2=1997

Solution for X2+y2=1997 equation:

X2+X2=1997

We move all terms to the left:

X2+X2-(1997)=0

We add all the numbers together, and all the variables

2X^2-1997=0

a = 2; b = 0; c = -1997;
Δ = b2-4ac
Δ = 02-4·2·(-1997)
Δ = 15976
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:

$\sqrt{\Delta}=\sqrt{15976}=\sqrt{4*3994}=\sqrt{4}*\sqrt{3994}=2\sqrt{3994}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3994}}{2*2}=\frac{0-2\sqrt{3994}}{4}
=-\frac{2\sqrt{3994}}{4}
=-\frac{\sqrt{3994}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3994}}{2*2}=\frac{0+2\sqrt{3994}}{4}
=\frac{2\sqrt{3994}}{4}
=\frac{\sqrt{3994}}{2}
$