X^2+y^2=1001

Solution for X^2+y^2=1001 equation:

X^2+X^2=1001

We move all terms to the left:

X^2+X^2-(1001)=0

We add all the numbers together, and all the variables

2X^2-1001=0

a = 2; b = 0; c = -1001;
Δ = b2-4ac
Δ = 02-4·2·(-1001)
Δ = 8008
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:

$\sqrt{\Delta}=\sqrt{8008}=\sqrt{4*2002}=\sqrt{4}*\sqrt{2002}=2\sqrt{2002}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2002}}{2*2}=\frac{0-2\sqrt{2002}}{4}
=-\frac{2\sqrt{2002}}{4}
=-\frac{\sqrt{2002}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2002}}{2*2}=\frac{0+2\sqrt{2002}}{4}
=\frac{2\sqrt{2002}}{4}
=\frac{\sqrt{2002}}{2}
$