x^2+x^2=12.25

Solution for x^2+x^2=12.25 equation:

x^2+x^2=12.25

We move all terms to the left:

x^2+x^2-(12.25)=0

We add all the numbers together, and all the variables

2x^2-12.25=0

a = 2; b = 0; c = -12.25;
Δ = b2-4ac
Δ = 02-4·2·(-12.25)
Δ = 98
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:

$\sqrt{\Delta}=\sqrt{98}=\sqrt{49*2}=\sqrt{49}*\sqrt{2}=7\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-7\sqrt{2}}{2*2}=\frac{0-7\sqrt{2}}{4}
=-\frac{7\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+7\sqrt{2}}{2*2}=\frac{0+7\sqrt{2}}{4}
=\frac{7\sqrt{2}}{4}
$