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(x²+2x)+1=0 equation

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Numerical solution:

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The solution

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 2              
x  + 2*x + 1 = 0
$$\left(x^{2} + 2 x\right) + 1 = 0$$
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
$$a = 1$$
$$b = 2$$
$$c = 1$$
, then
D = b^2 - 4 * a * c = 

(2)^2 - 4 * (1) * (1) = 0

Because D = 0, then the equation has one root.
x = -b/2a = -2/2/(1)

$$x_{1} = -1$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = 1$$
The graph
Rapid solution [src]
x1 = -1
$$x_{1} = -1$$
x1 = -1
Sum and product of roots [src]
sum
-1
$$-1$$
=
-1
$$-1$$
product
-1
$$-1$$
=
-1
$$-1$$
-1
Numerical answer [src]
x1 = -1.0
x1 = -1.0