X^2+x^2=200000000

Solution for X^2+x^2=200000000 equation:

X^2+X^2=200000000

We move all terms to the left:

X^2+X^2-(200000000)=0

We add all the numbers together, and all the variables

2X^2-200000000=0

a = 2; b = 0; c = -200000000;
Δ = b2-4ac
Δ = 02-4·2·(-200000000)
Δ = 1600000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600000000}=40000$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40000}{2*2}=\frac{-40000}{4}
=-10000
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40000}{2*2}=\frac{40000}{4}
=10000
$