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x^2-14*x-5=0 equation

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Numerical solution:

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The solution

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 2               
x  - 14*x - 5 = 0
$$\left(x^{2} - 14 x\right) - 5 = 0$$
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
$$a = 1$$
$$b = -14$$
$$c = -5$$
, then
D = b^2 - 4 * a * c = 

(-14)^2 - 4 * (1) * (-5) = 216

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

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

or
$$x_{1} = 7 + 3 \sqrt{6}$$
$$x_{2} = 7 - 3 \sqrt{6}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -14$$
$$q = \frac{c}{a}$$
$$q = -5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 14$$
$$x_{1} x_{2} = -5$$
Rapid solution [src]
             ___
x1 = 7 - 3*\/ 6 
$$x_{1} = 7 - 3 \sqrt{6}$$
             ___
x2 = 7 + 3*\/ 6 
$$x_{2} = 7 + 3 \sqrt{6}$$
x2 = 7 + 3*sqrt(6)
Sum and product of roots [src]
sum
        ___           ___
7 - 3*\/ 6  + 7 + 3*\/ 6 
$$\left(7 - 3 \sqrt{6}\right) + \left(7 + 3 \sqrt{6}\right)$$
=
14
$$14$$
product
/        ___\ /        ___\
\7 - 3*\/ 6 /*\7 + 3*\/ 6 /
$$\left(7 - 3 \sqrt{6}\right) \left(7 + 3 \sqrt{6}\right)$$
=
-5
$$-5$$
-5
Numerical answer [src]
x1 = 14.3484692283495
x2 = -0.348469228349534
x2 = -0.348469228349534