x2=31/121

Solution for x2=31/121 equation:

x2=31/121

We move all terms to the left:

x2-(31/121)=0

We add all the numbers together, and all the variables

x2-(+31/121)=0

We add all the numbers together, and all the variables

x^2-(+31/121)=0

We get rid of parentheses

x^2-31/121=0

We multiply all the terms by the denominator


x^2*121-31=0

Wy multiply elements

121x^2-31=0

a = 121; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·121·(-31)
Δ = 15004
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:

$\sqrt{\Delta}=\sqrt{15004}=\sqrt{484*31}=\sqrt{484}*\sqrt{31}=22\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{31}}{2*121}=\frac{0-22\sqrt{31}}{242}
=-\frac{22\sqrt{31}}{242}
=-\frac{\sqrt{31}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{31}}{2*121}=\frac{0+22\sqrt{31}}{242}
=\frac{22\sqrt{31}}{242}
=\frac{\sqrt{31}}{11}
$