x^2+x^2=31.5

Solution for x^2+x^2=31.5 equation:

x^2+x^2=31.5

We move all terms to the left:

x^2+x^2-(31.5)=0

We add all the numbers together, and all the variables

2x^2-31.5=0

a = 2; b = 0; c = -31.5;
Δ = b2-4ac
Δ = 02-4·2·(-31.5)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{7}}{2*2}=\frac{0-6\sqrt{7}}{4}
=-\frac{6\sqrt{7}}{4}
=-\frac{3\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{7}}{2*2}=\frac{0+6\sqrt{7}}{4}
=\frac{6\sqrt{7}}{4}
=\frac{3\sqrt{7}}{2}
$