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x^2+5x+9=0

x^2+5x+9=0 equation

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Numerical solution:

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The solution

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 2              
x  + 5*x + 9 = 0
x2+5x+9=0x^{2} + 5 x + 9 = 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=5b = 5
c=9c = 9
, then
D = b^2 - 4 * a * c = 

(5)^2 - 4 * (1) * (9) = -11

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=−52+11i2x_{1} = - \frac{5}{2} + \frac{\sqrt{11} i}{2}
Simplify
x2=−52−11i2x_{2} = - \frac{5}{2} - \frac{\sqrt{11} i}{2}
Simplify
Vieta's Theorem
it is reduced quadratic equation
px+x2+q=0p x + x^{2} + q = 0
where
p=bap = \frac{b}{a}
p=5p = 5
q=caq = \frac{c}{a}
q=9q = 9
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−5x_{1} + x_{2} = -5
x1x2=9x_{1} x_{2} = 9
The graph
012-9-8-7-6-5-4-3-2-1020
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
              ____             ____
      5   I*\/ 11      5   I*\/ 11 
0 + - - - -------- + - - + --------
      2      2         2      2
(0−(52+11i2))−(52−11i2)\left(0 - \left(\frac{5}{2} + \frac{\sqrt{11} i}{2}\right)\right) - \left(\frac{5}{2} - \frac{\sqrt{11} i}{2}\right) 
=
-5
−5-5 
product
  /          ____\ /          ____\
  |  5   I*\/ 11 | |  5   I*\/ 11 |
1*|- - - --------|*|- - + --------|
  \  2      2    / \  2      2    /
1(−52−11i2)(−52+11i2)1 \left(- \frac{5}{2} - \frac{\sqrt{11} i}{2}\right) \left(- \frac{5}{2} + \frac{\sqrt{11} i}{2}\right) 
=
9
99 
9
Rapid solution [src] 
               ____
       5   I*\/ 11 
x1 = - - - --------
       2      2
x1=−52−11i2x_{1} = - \frac{5}{2} - \frac{\sqrt{11} i}{2}
Simplify 
               ____
       5   I*\/ 11 
x2 = - - + --------
       2      2
x2=−52+11i2x_{2} = - \frac{5}{2} + \frac{\sqrt{11} i}{2}
Simplify
Numerical answer [src] 
x1 = -2.5 - 1.6583123951777*i
x2 = -2.5 + 1.6583123951777*i
x2 = -2.5 + 1.6583123951777*i
The graph
x^2+5x+9=0 equation
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