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Equation:
Equation (-5*x-3)*(2*x-1)=0
Equation (x+6)^3=25*(x+6)
Equation 10*(x-9)=7
Equation x^2-y^2=0
Express {x} in terms of y where:
-10*x+16*y=-6
-17*x+13*y=-3
12*x+14*y=-15
17*x+16*y=7
Graphing y =:
x^3-3x^2+5
Integral of d{x}:
x^3-3x^2+5
Identical expressions
x^ three -3x^ two + five
x cubed minus 3x squared plus 5
x to the power of three minus 3x to the power of two plus five
x3-3x2+5
x³-3x²+5
x to the power of 3-3x to the power of 2+5
Similar expressions
x^3-3x^2-5
x^3+3x^2+5

x^3-3x^2+5 equation

The teacher will be very surprised to see your correct solution 😉

The solution

You have entered [src]

 3      2        
x  - 3*x  + 5 = 0

x^{3} - 3 x^{2} + 5 = 0

Simplify

Vieta's Theorem

it is reduced cubic equation

p x^{2} + x^{3} + q x + v = 0

where

p = \frac{b}{a}

p = -3

q = \frac{c}{a}

q = 0

v = \frac{d}{a}

v = 5

Vieta Formulas

x_{1} + x_{2} + x_{3} = - p

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q

x_{1} x_{2} x_{3} = v

x_{1} + x_{2} + x_{3} = 3

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0

x_{1} x_{2} x_{3} = 5

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

              _______________                              /                                      _______________\
             /           ___                               |                                     /           ___ |
            /  81   27*\/ 5                                |                             ___    /  81   27*\/ 5  |
         3 /   -- + --------                               |             ___           \/ 3 *3 /   -- + -------- |
         \/    2       2                  3                |         3*\/ 3                  \/    2       2     |
x1 = 1 + -------------------- + ---------------------- + I*|- ---------------------- + --------------------------|
                  6                    _______________     |         _______________               6             |
                                      /           ___      |        /           ___                              |
                                     /  81   27*\/ 5       |       /  81   27*\/ 5                               |
                                2*3 /   -- + --------      |  2*3 /   -- + --------                              |
                                  \/    2       2          \    \/    2       2                                  /

x_{1} = \frac{3}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6} + 1 + i \left(- \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6}\right)

Simplify

              _______________                              /             _______________                         \
             /           ___                               |            /           ___                          |
            /  81   27*\/ 5                                |    ___    /  81   27*\/ 5                           |
         3 /   -- + --------                               |  \/ 3 *3 /   -- + --------               ___        |
         \/    2       2                  3                |        \/    2       2               3*\/ 3         |
x2 = 1 + -------------------- + ---------------------- + I*|- -------------------------- + ----------------------|
                  6                    _______________     |              6                       _______________|
                                      /           ___      |                                     /           ___ |
                                     /  81   27*\/ 5       |                                    /  81   27*\/ 5  |
                                2*3 /   -- + --------      |                               2*3 /   -- + -------- |
                                  \/    2       2          \                                 \/    2       2     /

x_{2} = \frac{3}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6} + \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}\right)

Simplify

                                     _______________
                                    /           ___ 
                                   /  81   27*\/ 5  
                                3 /   -- + -------- 
                  3             \/    2       2     
x3 = 1 - -------------------- - --------------------
              _______________            3          
             /           ___                        
            /  81   27*\/ 5                         
         3 /   -- + --------                        
         \/    2       2

x_{3} = - \frac{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + 1

Simplify

Sum and product of roots [src]

sum

             _______________                              /                                      _______________\            _______________                              /             _______________                         \                                   _______________
            /           ___                               |                                     /           ___ |           /           ___                               |            /           ___                          |                                  /           ___ 
           /  81   27*\/ 5                                |                             ___    /  81   27*\/ 5  |          /  81   27*\/ 5                                |    ___    /  81   27*\/ 5                           |                                 /  81   27*\/ 5  
        3 /   -- + --------                               |             ___           \/ 3 *3 /   -- + -------- |       3 /   -- + --------                               |  \/ 3 *3 /   -- + --------               ___        |                              3 /   -- + -------- 
        \/    2       2                  3                |         3*\/ 3                  \/    2       2     |       \/    2       2                  3                |        \/    2       2               3*\/ 3         |                3             \/    2       2     
0 + 1 + -------------------- + ---------------------- + I*|- ---------------------- + --------------------------| + 1 + -------------------- + ---------------------- + I*|- -------------------------- + ----------------------| + 1 - -------------------- - --------------------
                 6                    _______________     |         _______________               6             |                6                    _______________     |              6                       _______________|            _______________            3          
                                     /           ___      |        /           ___                              |                                    /           ___      |                                     /           ___ |           /           ___                        
                                    /  81   27*\/ 5       |       /  81   27*\/ 5                               |                                   /  81   27*\/ 5       |                                    /  81   27*\/ 5  |          /  81   27*\/ 5                         
                               2*3 /   -- + --------      |  2*3 /   -- + --------                              |                              2*3 /   -- + --------      |                               2*3 /   -- + -------- |       3 /   -- + --------                        
                                 \/    2       2          \    \/    2       2                                  /                                \/    2       2          \                                 \/    2       2     /       \/    2       2

\left(- \frac{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + 1\right) + \left(\left(\frac{3}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6} + \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}\right)\right) + \left(0 + \left(\frac{3}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6} + 1 + i \left(- \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6}\right)\right)\right)\right)

      /                                      _______________\     /             _______________                         \
      |                                     /           ___ |     |            /           ___                          |
      |                             ___    /  81   27*\/ 5  |     |    ___    /  81   27*\/ 5                           |
      |             ___           \/ 3 *3 /   -- + -------- |     |  \/ 3 *3 /   -- + --------               ___        |
      |         3*\/ 3                  \/    2       2     |     |        \/    2       2               3*\/ 3         |
3 + I*|- ---------------------- + --------------------------| + I*|- -------------------------- + ----------------------|
      |         _______________               6             |     |              6                       _______________|
      |        /           ___                              |     |                                     /           ___ |
      |       /  81   27*\/ 5                               |     |                                    /  81   27*\/ 5  |
      |  2*3 /   -- + --------                              |     |                               2*3 /   -- + -------- |
      \    \/    2       2                                  /     \                                 \/    2       2     /

3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6} + \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}\right) + i \left(- \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6}\right)

product

  /         _______________                              /                                      _______________\\ /         _______________                              /             _______________                         \\ /                                _______________\
  |        /           ___                               |                                     /           ___ || |        /           ___                               |            /           ___                          || |                               /           ___ |
  |       /  81   27*\/ 5                                |                             ___    /  81   27*\/ 5  || |       /  81   27*\/ 5                                |    ___    /  81   27*\/ 5                           || |                              /  81   27*\/ 5  |
  |    3 /   -- + --------                               |             ___           \/ 3 *3 /   -- + -------- || |    3 /   -- + --------                               |  \/ 3 *3 /   -- + --------               ___        || |                           3 /   -- + -------- |
  |    \/    2       2                  3                |         3*\/ 3                  \/    2       2     || |    \/    2       2                  3                |        \/    2       2               3*\/ 3         || |             3             \/    2       2     |
1*|1 + -------------------- + ---------------------- + I*|- ---------------------- + --------------------------||*|1 + -------------------- + ---------------------- + I*|- -------------------------- + ----------------------||*|1 - -------------------- - --------------------|
  |             6                    _______________     |         _______________               6             || |             6                    _______________     |              6                       _______________|| |         _______________            3          |
  |                                 /           ___      |        /           ___                              || |                                 /           ___      |                                     /           ___ || |        /           ___                        |
  |                                /  81   27*\/ 5       |       /  81   27*\/ 5                               || |                                /  81   27*\/ 5       |                                    /  81   27*\/ 5  || |       /  81   27*\/ 5                         |
  |                           2*3 /   -- + --------      |  2*3 /   -- + --------                              || |                           2*3 /   -- + --------      |                               2*3 /   -- + -------- || |    3 /   -- + --------                        |
  \                             \/    2       2          \    \/    2       2                                  // \                             \/    2       2          \                                 \/    2       2     // \    \/    2       2                            /

1 \cdot \left(\frac{3}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6} + 1 + i \left(- \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6}\right)\right) \left(\frac{3}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{6} + \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + 1\right)

-5

-5

-5

Numerical answer [src]

x1 = -1.10380340273554

x2 = 2.05190170136777 - 0.565235851677171*i

x3 = 2.05190170136777 + 0.565235851677171*i

x3 = 2.05190170136777 + 0.565235851677171*i

The graph

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Identical expressions

Similar expressions

x^3-3x^2+5 equation

Numerical solution:

The solution