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x^2-4*x+2=0

x^2-4*x+2=0 equation

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Numerical solution:

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The solution

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 2              
x  - 4*x + 2 = 0
(x2−4x)+2=0\left(x^{2} - 4 x\right) + 2 = 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=2c = 2
, then
D = b^2 - 4 * a * c = 

(-4)^2 - 4 * (1) * (2) = 8

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

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

or
x1=2+2x_{1} = \sqrt{2} + 2
x2=2−2x_{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=2q = 2
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=4x_{1} + x_{2} = 4
x1x2=2x_{1} x_{2} = 2
The graph
05-10-5101520200-100
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
           ___
x1 = 2 - \/ 2
x1=2−2x_{1} = 2 - \sqrt{2} 
           ___
x2 = 2 + \/ 2
x2=2+2x_{2} = \sqrt{2} + 2 
x2 = sqrt(2) + 2
Sum and product of roots [src] 
sum
      ___         ___
2 - \/ 2  + 2 + \/ 2
(2−2)+(2+2)\left(2 - \sqrt{2}\right) + \left(\sqrt{2} + 2\right) 
=
4
44 
product
/      ___\ /      ___\
\2 - \/ 2 /*\2 + \/ 2 /
(2−2)(2+2)\left(2 - \sqrt{2}\right) \left(\sqrt{2} + 2\right) 
=
2
22 
2
Numerical answer [src] 
x1 = 0.585786437626905
x2 = 3.41421356237309
x2 = 3.41421356237309
The graph
x^2-4*x+2=0 equation
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