x2+18x=-31

Solution for x2+18x=-31 equation:

x2+18x=-31

We move all terms to the left:

x2+18x-(-31)=0

We add all the numbers together, and all the variables

x^2+18x+31=0

a = 1; b = 18; c = +31;
Δ = b2-4ac
Δ = 182-4·1·31
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10\sqrt{2}}{2*1}=\frac{-18-10\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10\sqrt{2}}{2*1}=\frac{-18+10\sqrt{2}}{2}
$