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x^2-16*x+4=0 equation

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Numerical solution:

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The solution

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 2               
x  - 16*x + 4 = 0
(x2−16x)+4=0\left(x^{2} - 16 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=−16b = -16
c=4c = 4
, then
D = b^2 - 4 * a * c = 

(-16)^2 - 4 * (1) * (4) = 240

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

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

or
x1=215+8x_{1} = 2 \sqrt{15} + 8
x2=8−215x_{2} = 8 - 2 \sqrt{15}
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−16p = -16
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=16x_{1} + x_{2} = 16
x1x2=4x_{1} x_{2} = 4
Sum and product of roots [src] 
sum
        ____           ____
8 - 2*\/ 15  + 8 + 2*\/ 15
(8−215)+(215+8)\left(8 - 2 \sqrt{15}\right) + \left(2 \sqrt{15} + 8\right) 
=
16
1616 
product
/        ____\ /        ____\
\8 - 2*\/ 15 /*\8 + 2*\/ 15 /
(8−215)(215+8)\left(8 - 2 \sqrt{15}\right) \left(2 \sqrt{15} + 8\right) 
=
4
44 
4
Rapid solution [src] 
             ____
x1 = 8 - 2*\/ 15
x1=8−215x_{1} = 8 - 2 \sqrt{15} 
             ____
x2 = 8 + 2*\/ 15
x2=215+8x_{2} = 2 \sqrt{15} + 8 
x2 = 2*sqrt(15) + 8
Numerical answer [src] 
x1 = 0.254033307585166
x2 = 15.7459666924148
x2 = 15.7459666924148
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