X^2+x^2=1012.5

Solution for X^2+x^2=1012.5 equation:

X^2+X^2=1012.5

We move all terms to the left:

X^2+X^2-(1012.5)=0

We add all the numbers together, and all the variables

2X^2-1012.5=0

a = 2; b = 0; c = -1012.5;
Δ = b2-4ac
Δ = 02-4·2·(-1012.5)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90}{2*2}=\frac{-90}{4}
=-22+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90}{2*2}=\frac{90}{4}
=22+1/2
$