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x^2+4*x+6=0

x^2+4*x+6=0 equation

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Numerical solution:

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The solution

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 2              
x  + 4*x + 6 = 0
(x2+4x)+6=0\left(x^{2} + 4 x\right) + 6 = 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=4b = 4
c=6c = 6
, then
D = b^2 - 4 * a * c = 

(4)^2 - 4 * (1) * (6) = -8

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=−2+2ix_{1} = -2 + \sqrt{2} i
x2=−2−2ix_{2} = -2 - \sqrt{2} 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=4p = 4
q=caq = \frac{c}{a}
q=6q = 6
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−4x_{1} + x_{2} = -4
x1x2=6x_{1} x_{2} = 6
The graph
0123-8-7-6-5-4-3-2-1020
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
              ___
x1 = -2 - I*\/ 2
x1=−2−2ix_{1} = -2 - \sqrt{2} i 
              ___
x2 = -2 + I*\/ 2
x2=−2+2ix_{2} = -2 + \sqrt{2} i 
x2 = -2 + sqrt(2)*i
Sum and product of roots [src] 
sum
         ___            ___
-2 - I*\/ 2  + -2 + I*\/ 2
(−2−2i)+(−2+2i)\left(-2 - \sqrt{2} i\right) + \left(-2 + \sqrt{2} i\right) 
=
-4
−4-4 
product
/         ___\ /         ___\
\-2 - I*\/ 2 /*\-2 + I*\/ 2 /
(−2−2i)(−2+2i)\left(-2 - \sqrt{2} i\right) \left(-2 + \sqrt{2} i\right) 
=
6
66 
6
Numerical answer [src] 
x1 = -2.0 - 1.4142135623731*i
x2 = -2.0 + 1.4142135623731*i
x2 = -2.0 + 1.4142135623731*i
The graph
x^2+4*x+6=0 equation
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