X^2+x^2=165^2

Solution for X^2+x^2=165^2 equation:

X^2+X^2=165^2

We move all terms to the left:

X^2+X^2-(165^2)=0

We add all the numbers together, and all the variables

2X^2-27225=0

a = 2; b = 0; c = -27225;
Δ = b2-4ac
Δ = 02-4·2·(-27225)
Δ = 217800
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:

$\sqrt{\Delta}=\sqrt{217800}=\sqrt{108900*2}=\sqrt{108900}*\sqrt{2}=330\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-330\sqrt{2}}{2*2}=\frac{0-330\sqrt{2}}{4}
=-\frac{330\sqrt{2}}{4}
=-\frac{165\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+330\sqrt{2}}{2*2}=\frac{0+330\sqrt{2}}{4}
=\frac{330\sqrt{2}}{4}
=\frac{165\sqrt{2}}{2}
$