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x^3-3.24x=0

x^3-3.24x=0 equation

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Numerical solution:

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The solution

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 3   81*x    
x  - ---- = 0
      25     
x381x25=0x^{3} - \frac{81 x}{25} = 0
Detail solution
Given the equation:
x381x25=0x^{3} - \frac{81 x}{25} = 0
transform
Take common factor x from the equation
we get:
x(x28125)=0x \left(x^{2} - \frac{81}{25}\right) = 0
then:
x1=0x_{1} = 0
and also
we get the equation
x28125=0x^{2} - \frac{81}{25} = 0
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:
x2=Db2ax_{2} = \frac{\sqrt{D} - b}{2 a}
x3=Db2ax_{3} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=0b = 0
c=8125c = - \frac{81}{25}
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (-81/25) = 324/25

Because D > 0, then the equation has two roots.
x2 = (-b + sqrt(D)) / (2*a)

x3 = (-b - sqrt(D)) / (2*a)

or
x2=95x_{2} = \frac{9}{5}
Simplify
x3=95x_{3} = - \frac{9}{5}
Simplify
The final answer for (x^3 - 81*x/25) + 0 = 0:
x1=0x_{1} = 0
x2=95x_{2} = \frac{9}{5}
x3=95x_{3} = - \frac{9}{5}
Vieta's Theorem
it is reduced cubic equation
px2+x3+qx+v=0p x^{2} + x^{3} + q x + v = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=8125q = - \frac{81}{25}
v=dav = \frac{d}{a}
v=0v = 0
Vieta Formulas
x1+x2+x3=px_{1} + x_{2} + x_{3} = - p
x1x2+x1x3+x2x3=qx_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q
x1x2x3=vx_{1} x_{2} x_{3} = v
x1+x2+x3=0x_{1} + x_{2} + x_{3} = 0
x1x2+x1x3+x2x3=8125x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{81}{25}
x1x2x3=0x_{1} x_{2} x_{3} = 0
The graph
05-15-10-51015-50005000
Rapid solution [src]
x1 = -9/5
x1=95x_{1} = - \frac{9}{5}
x2 = 0
x2=0x_{2} = 0
x3 = 9/5
x3=95x_{3} = \frac{9}{5}
Sum and product of roots [src]
sum
0 - 9/5 + 0 + 9/5
((95+0)+0)+95\left(\left(- \frac{9}{5} + 0\right) + 0\right) + \frac{9}{5}
=
0
00
product
1*-9/5*0*9/5
1(95)0951 \left(- \frac{9}{5}\right) 0 \cdot \frac{9}{5}
=
0
00
0
Numerical answer [src]
x1 = -1.8
x2 = 0.0
x3 = 1.8
x3 = 1.8
The graph
x^3-3.24x=0 equation