a^2+a^2=2500

Solution for a^2+a^2=2500 equation:

a^2+a^2=2500

We move all terms to the left:

a^2+a^2-(2500)=0

We add all the numbers together, and all the variables

2a^2-2500=0

a = 2; b = 0; c = -2500;
Δ = b2-4ac
Δ = 02-4·2·(-2500)
Δ = 20000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20000}=\sqrt{10000*2}=\sqrt{10000}*\sqrt{2}=100\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{2}}{2*2}=\frac{0-100\sqrt{2}}{4}
=-\frac{100\sqrt{2}}{4}
=-25\sqrt{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{2}}{2*2}=\frac{0+100\sqrt{2}}{4}
=\frac{100\sqrt{2}}{4}
=25\sqrt{2}
$