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x^2-3*x-3=0

x^2-3*x-3=0 equation

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Numerical solution:

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The solution

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 2              
x  - 3*x - 3 = 0
$$\left(x^{2} - 3 x\right) - 3 = 0$$
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
$$a = 1$$
$$b = -3$$
$$c = -3$$
, then
D = b^2 - 4 * a * c = 

(-3)^2 - 4 * (1) * (-3) = 21

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

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

or
$$x_{1} = \frac{3}{2} + \frac{\sqrt{21}}{2}$$
$$x_{2} = \frac{3}{2} - \frac{\sqrt{21}}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 3$$
$$x_{1} x_{2} = -3$$
The graph
Rapid solution [src]
           ____
     3   \/ 21 
x1 = - - ------
     2     2   
$$x_{1} = \frac{3}{2} - \frac{\sqrt{21}}{2}$$
           ____
     3   \/ 21 
x2 = - + ------
     2     2   
$$x_{2} = \frac{3}{2} + \frac{\sqrt{21}}{2}$$
x2 = 3/2 + sqrt(21)/2
Sum and product of roots [src]
sum
      ____         ____
3   \/ 21    3   \/ 21 
- - ------ + - + ------
2     2      2     2   
$$\left(\frac{3}{2} - \frac{\sqrt{21}}{2}\right) + \left(\frac{3}{2} + \frac{\sqrt{21}}{2}\right)$$
=
3
$$3$$
product
/      ____\ /      ____\
|3   \/ 21 | |3   \/ 21 |
|- - ------|*|- + ------|
\2     2   / \2     2   /
$$\left(\frac{3}{2} - \frac{\sqrt{21}}{2}\right) \left(\frac{3}{2} + \frac{\sqrt{21}}{2}\right)$$
=
-3
$$-3$$
-3
Numerical answer [src]
x1 = 3.79128784747792
x2 = -0.79128784747792
x2 = -0.79128784747792
The graph
x^2-3*x-3=0 equation