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x^2+5x+6=0

x^2+5x+6=0 equation

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Numerical solution:

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The solution

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 2              
x  + 5*x + 6 = 0
$$\left(x^{2} + 5 x\right) + 6 = 0$$
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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 5$$
$$c = 6$$
, then
D = b^2 - 4 * a * c = 

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

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

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

or
$$x_{1} = -2$$
$$x_{2} = -3$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 5$$
$$q = \frac{c}{a}$$
$$q = 6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -5$$
$$x_{1} x_{2} = 6$$
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-3 - 2
$$-3 - 2$$ 
=
-5
$$-5$$ 
product
-3*(-2)
$$- -6$$ 
=
6
$$6$$ 
6
Rapid solution [src] 
x1 = -3
$$x_{1} = -3$$ 
x2 = -2
$$x_{2} = -2$$ 
x2 = -2
Numerical answer [src] 
x1 = -3.0
x2 = -2.0
x2 = -2.0
The graph
x^2+5x+6=0 equation
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