x^2+x^2=16^2

Solution for x^2+x^2=16^2 equation:

x^2+x^2=16^2

We move all terms to the left:

x^2+x^2-(16^2)=0

We add all the numbers together, and all the variables

2x^2-256=0

a = 2; b = 0; c = -256;
Δ = b2-4ac
Δ = 02-4·2·(-256)
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{2}}{2*2}=\frac{0-32\sqrt{2}}{4}
=-\frac{32\sqrt{2}}{4}
=-8\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{2}}{2*2}=\frac{0+32\sqrt{2}}{4}
=\frac{32\sqrt{2}}{4}
=8\sqrt{2}
$