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x^2+4x-4=0

x^2+4x-4=0 equation

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Numerical solution:

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The solution

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

(4)^2 - 4 * (1) * (-4) = 32

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

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

or
$$x_{1} = -2 + 2 \sqrt{2}$$
$$x_{2} = - 2 \sqrt{2} - 2$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = -4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = -4$$
The graph
Rapid solution [src]
              ___
x1 = -2 + 2*\/ 2 
$$x_{1} = -2 + 2 \sqrt{2}$$
              ___
x2 = -2 - 2*\/ 2 
$$x_{2} = - 2 \sqrt{2} - 2$$
x2 = -2*sqrt(2) - 2
Sum and product of roots [src]
sum
         ___            ___
-2 + 2*\/ 2  + -2 - 2*\/ 2 
$$\left(- 2 \sqrt{2} - 2\right) + \left(-2 + 2 \sqrt{2}\right)$$
=
-4
$$-4$$
product
/         ___\ /         ___\
\-2 + 2*\/ 2 /*\-2 - 2*\/ 2 /
$$\left(-2 + 2 \sqrt{2}\right) \left(- 2 \sqrt{2} - 2\right)$$
=
-4
$$-4$$
-4
Numerical answer [src]
x1 = -4.82842712474619
x2 = 0.82842712474619
x2 = 0.82842712474619
The graph
x^2+4x-4=0 equation