X^2+y^2=42.25

Solution for X^2+y^2=42.25 equation:

X^2+X^2=42.25

We move all terms to the left:

X^2+X^2-(42.25)=0

We add all the numbers together, and all the variables

2X^2-42.25=0

a = 2; b = 0; c = -42.25;
Δ = b2-4ac
Δ = 02-4·2·(-42.25)
Δ = 338
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:

$\sqrt{\Delta}=\sqrt{338}=\sqrt{169*2}=\sqrt{169}*\sqrt{2}=13\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-13\sqrt{2}}{2*2}=\frac{0-13\sqrt{2}}{4}
=-\frac{13\sqrt{2}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+13\sqrt{2}}{2*2}=\frac{0+13\sqrt{2}}{4}
=\frac{13\sqrt{2}}{4}
$