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x^2+6x+5 equation

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Numerical solution:

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The solution

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x  + 6*x + 5 = 0
(x2+6x)+5=0\left(x^{2} + 6 x\right) + 5 = 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=6b = 6
c=5c = 5
, then
D = b^2 - 4 * a * c = 

(6)^2 - 4 * (1) * (5) = 16

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

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

or
x1=−1x_{1} = -1
x2=−5x_{2} = -5
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=6p = 6
q=caq = \frac{c}{a}
q=5q = 5
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−6x_{1} + x_{2} = -6
x1x2=5x_{1} x_{2} = 5
The graph
05-20-15-10-510-200200
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -5
x1=−5x_{1} = -5 
x2 = -1
x2=−1x_{2} = -1 
x2 = -1
Sum and product of roots [src] 
sum
-5 - 1
−5−1-5 - 1 
=
-6
−6-6 
product
-5*(-1)
−−5- -5 
=
5
55 
5
Numerical answer [src] 
x1 = -5.0
x2 = -1.0
x2 = -1.0
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