x^2+x^2=52

Solution for x^2+x^2=52 equation:

x^2+x^2=52

We move all terms to the left:

x^2+x^2-(52)=0

We add all the numbers together, and all the variables

2x^2-52=0

a = 2; b = 0; c = -52;
Δ = b2-4ac
Δ = 02-4·2·(-52)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{26}}{2*2}=\frac{0-4\sqrt{26}}{4}
=-\frac{4\sqrt{26}}{4}
=-\sqrt{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{26}}{2*2}=\frac{0+4\sqrt{26}}{4}
=\frac{4\sqrt{26}}{4}
=\sqrt{26}
$