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x^2+2x+15=0 equation

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Numerical solution:

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The solution

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 2               
x  + 2*x + 15 = 0
(x2+2x)+15=0\left(x^{2} + 2 x\right) + 15 = 0
Simplify
Detail solution
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=2b = 2
c=15c = 15
, then
D = b^2 - 4 * a * c = 

(2)^2 - 4 * (1) * (15) = -56

Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=−1+14ix_{1} = -1 + \sqrt{14} i
x2=−1−14ix_{2} = -1 - \sqrt{14} i
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=2p = 2
q=caq = \frac{c}{a}
q=15q = 15
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−2x_{1} + x_{2} = -2
x1x2=15x_{1} x_{2} = 15
The graph
-4.5-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.5020
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
         ____            ____
-1 - I*\/ 14  + -1 + I*\/ 14
(−1−14i)+(−1+14i)\left(-1 - \sqrt{14} i\right) + \left(-1 + \sqrt{14} i\right) 
=
-2
−2-2 
product
/         ____\ /         ____\
\-1 - I*\/ 14 /*\-1 + I*\/ 14 /
(−1−14i)(−1+14i)\left(-1 - \sqrt{14} i\right) \left(-1 + \sqrt{14} i\right) 
=
15
1515 
15
Rapid solution [src] 
              ____
x1 = -1 - I*\/ 14
x1=−1−14ix_{1} = -1 - \sqrt{14} i 
              ____
x2 = -1 + I*\/ 14
x2=−1+14ix_{2} = -1 + \sqrt{14} i 
x2 = -1 + sqrt(14)*i
Numerical answer [src] 
x1 = -1.0 - 3.74165738677394*i
x2 = -1.0 + 3.74165738677394*i
x2 = -1.0 + 3.74165738677394*i
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