x^2+x^2=289

Solution for x^2+x^2=289 equation:

x^2+x^2=289

We move all terms to the left:

x^2+x^2-(289)=0

We add all the numbers together, and all the variables

2x^2-289=0

a = 2; b = 0; c = -289;
Δ = b2-4ac
Δ = 02-4·2·(-289)
Δ = 2312
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:

$\sqrt{\Delta}=\sqrt{2312}=\sqrt{1156*2}=\sqrt{1156}*\sqrt{2}=34\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-34\sqrt{2}}{2*2}=\frac{0-34\sqrt{2}}{4}
=-\frac{34\sqrt{2}}{4}
=-\frac{17\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+34\sqrt{2}}{2*2}=\frac{0+34\sqrt{2}}{4}
=\frac{34\sqrt{2}}{4}
=\frac{17\sqrt{2}}{2}
$