X^2+22x+41=-64

Solution for X^2+22x+41=-64 equation:

X^2+22X+41=-64

We move all terms to the left:

X^2+22X+41-(-64)=0

We add all the numbers together, and all the variables

X^2+22X+105=0

a = 1; b = 22; c = +105;
Δ = b2-4ac
Δ = 222-4·1·105
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-8}{2*1}=\frac{-30}{2}
=-15
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+8}{2*1}=\frac{-14}{2}
=-7
$