x^2+x^2=2.5^2

Solution for x^2+x^2=2.5^2 equation:

x^2+x^2=2.5^2

We move all terms to the left:

x^2+x^2-(2.5^2)=0

We add all the numbers together, and all the variables

2x^2-6.25=0

a = 2; b = 0; c = -6.25;
Δ = b2-4ac
Δ = 02-4·2·(-6.25)
Δ = 50
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:

$\sqrt{\Delta}=\sqrt{50}=\sqrt{25*2}=\sqrt{25}*\sqrt{2}=5\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5\sqrt{2}}{2*2}=\frac{0-5\sqrt{2}}{4}
=-\frac{5\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5\sqrt{2}}{2*2}=\frac{0+5\sqrt{2}}{4}
=\frac{5\sqrt{2}}{4}
$