x^2+x^2=81

Solution for x^2+x^2=81 equation:

x^2+x^2=81

We move all terms to the left:

x^2+x^2-(81)=0

We add all the numbers together, and all the variables

2x^2-81=0

a = 2; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·2·(-81)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{2}}{2*2}=\frac{0-18\sqrt{2}}{4}
=-\frac{18\sqrt{2}}{4}
=-\frac{9\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{2}}{2*2}=\frac{0+18\sqrt{2}}{4}
=\frac{18\sqrt{2}}{4}
=\frac{9\sqrt{2}}{2}
$