x^2+x^2=1024

Solution for x^2+x^2=1024 equation:

x^2+x^2=1024

We move all terms to the left:

x^2+x^2-(1024)=0

We add all the numbers together, and all the variables

2x^2-1024=0

a = 2; b = 0; c = -1024;
Δ = b2-4ac
Δ = 02-4·2·(-1024)
Δ = 8192
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:

$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{2}}{2*2}=\frac{0-64\sqrt{2}}{4}
=-\frac{64\sqrt{2}}{4}
=-16\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{2}}{2*2}=\frac{0+64\sqrt{2}}{4}
=\frac{64\sqrt{2}}{4}
=16\sqrt{2}
$