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x²+2x+1=1 equation

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Numerical solution:

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The solution

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 2              
x  + 2*x + 1 = 1
(x2+2x)+1=1\left(x^{2} + 2 x\right) + 1 = 1
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
(x2+2x)+1=1\left(x^{2} + 2 x\right) + 1 = 1
to
((x2+2x)+1)−1=0\left(\left(x^{2} + 2 x\right) + 1\right) - 1 = 0
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=2b = 2
c=0c = 0
, then
D = b^2 - 4 * a * c = 

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

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

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

or
x1=0x_{1} = 0
x2=−2x_{2} = -2
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=2p = 2
q=caq = \frac{c}{a}
q=0q = 0
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−2x_{1} + x_{2} = -2
x1x2=0x_{1} x_{2} = 0
The graph
05-15-10-515100200
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -2
x1=−2x_{1} = -2 
x2 = 0
x2=0x_{2} = 0 
x2 = 0
Sum and product of roots [src] 
sum
-2
−2-2 
=
-2
−2-2 
product
-2*0
−0- 0 
=
0
00 
0
Numerical answer [src] 
x1 = -2.0
x2 = 0.0
x2 = 0.0
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