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x^2-4*x-4=0

x^2-4*x-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
(x2−4x)−4=0\left(x^{2} - 4 x\right) - 4 = 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=−4b = -4
c=−4c = -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
x1=2+22x_{1} = 2 + 2 \sqrt{2}
x2=2−22x_{2} = 2 - 2 \sqrt{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=−4p = -4
q=caq = \frac{c}{a}
q=−4q = -4
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=4x_{1} + x_{2} = 4
x1x2=−4x_{1} x_{2} = -4
The graph
05-15-10-5101520-200200
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
        ___           ___
2 - 2*\/ 2  + 2 + 2*\/ 2
(2−22)+(2+22)\left(2 - 2 \sqrt{2}\right) + \left(2 + 2 \sqrt{2}\right) 
=
4
44 
product
/        ___\ /        ___\
\2 - 2*\/ 2 /*\2 + 2*\/ 2 /
(2−22)(2+22)\left(2 - 2 \sqrt{2}\right) \left(2 + 2 \sqrt{2}\right) 
=
-4
−4-4 
-4
Rapid solution [src] 
             ___
x1 = 2 - 2*\/ 2
x1=2−22x_{1} = 2 - 2 \sqrt{2} 
             ___
x2 = 2 + 2*\/ 2
x2=2+22x_{2} = 2 + 2 \sqrt{2} 
x2 = 2 + 2*sqrt(2)
Numerical answer [src] 
x1 = -0.82842712474619
x2 = 4.82842712474619
x2 = 4.82842712474619
The graph
x^2-4*x-4=0 equation
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