x^2+x^2+1=113

Solution for x^2+x^2+1=113 equation:

x^2+x^2+1=113

We move all terms to the left:

x^2+x^2+1-(113)=0

We add all the numbers together, and all the variables

2x^2-112=0

a = 2; b = 0; c = -112;
Δ = b2-4ac
Δ = 02-4·2·(-112)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*2}=\frac{0-8\sqrt{14}}{4}
=-\frac{8\sqrt{14}}{4}
=-2\sqrt{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*2}=\frac{0+8\sqrt{14}}{4}
=\frac{8\sqrt{14}}{4}
=2\sqrt{14}
$