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Equation:
Equation x/4+13=x+1
Equation 4(x-8)=-5
Equation 3x-2=0
Equation x*8=25+15
Express {x} in terms of y where:
4*x+8*y=7
-14*x+5*y=3
13*x-18*y=-17
4*x+18*y=-7
Identical expressions
-x^(five)+ eight *x^(four)- twenty-two *x^(three)+ twenty-eight *x^(two)- twenty-four *x+ sixteen = zero
minus x to the power of (5) plus 8 multiply by x to the power of (4) minus 22 multiply by x to the power of (3) plus 28 multiply by x to the power of (2) minus 24 multiply by x plus 16 equally 0
minus x to the power of (five) plus eight multiply by x to the power of (four) minus twenty minus two multiply by x to the power of (three) plus twenty minus eight multiply by x to the power of (two) minus twenty minus four multiply by x plus sixteen equally zero
-x(5)+8*x(4)-22*x(3)+28*x(2)-24*x+16=0
-x5+8*x4-22*x3+28*x2-24*x+16=0
-x^(5)+8x^(4)-22x^(3)+28x^(2)-24x+16=0
-x(5)+8x(4)-22x(3)+28x(2)-24x+16=0
-x5+8x4-22x3+28x2-24x+16=0
-x^5+8x^4-22x^3+28x^2-24x+16=0
-x^(5)+8*x^(4)-22*x^(3)+28*x^(2)-24*x+16=O
Similar expressions
-x^(5)+8*x^(4)+22*x^(3)+28*x^(2)-24*x+16=0
-x^(5)+8*x^(4)-22*x^(3)+28*x^(2)+24*x+16=0
-x^(5)-8*x^(4)-22*x^(3)+28*x^(2)-24*x+16=0
x^(5)+8*x^(4)-22*x^(3)+28*x^(2)-24*x+16=0
-x^(5)+8*x^(4)-22*x^(3)+28*x^(2)-24*x-16=0
-x^(5)+8*x^(4)-22*x^(3)-28*x^(2)-24*x+16=0

-x^(5)+8x^(4)-22x^(3)+28x^(2)-24x+16=0 equation

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

The solution

You have entered [src]

   5      4       3       2                
- x  + 8*x  - 22*x  + 28*x  - 24*x + 16 = 0

$$\left(- 24 x + \left(28 x^{2} + \left(- 22 x^{3} + \left(- x^{5} + 8 x^{4}\right)\right)\right)\right) + 16 = 0$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Sum and product of roots [src]

sum

                                       ________________     /             ________________                          \                                      ________________     /           ________________                          \                                                      
                                      /          _____      |            /          _____                           |                                     /          _____      |          /          _____                           |                                                      
                                     /  82   2*\/ 159       |    ___    /  82   2*\/ 159                            |                                    /  82   2*\/ 159       |  ___    /  82   2*\/ 159                            |            ________________                          
                                  3 /   -- + ---------      |  \/ 3 *3 /   -- + ---------                ___        |                                 3 /   -- + ---------      |\/ 3 *3 /   -- + ---------                ___        |           /          _____                           
    4              5              \/    27       9          |        \/    27       9                5*\/ 3         |   4              5              \/    27       9          |      \/    27       9                5*\/ 3         |   4      /  82   2*\/ 159                10          
2 + - - ----------------------- - --------------------- + I*|- --------------------------- + -----------------------| + - - ----------------------- - --------------------- + I*|--------------------------- - -----------------------| + - + 3 /   -- + ---------  + -----------------------
    3          ________________             2               |               2                       ________________|   3          ________________             2               |             2                       ________________|   3   \/    27       9               ________________
              /          _____                              |                                      /          _____ |             /          _____                              |                                    /          _____ |                                     /          _____ 
             /  82   2*\/ 159                               |                                     /  82   2*\/ 159  |            /  82   2*\/ 159                               |                                   /  82   2*\/ 159  |                                    /  82   2*\/ 159  
        9*3 /   -- + ---------                              |                                9*3 /   -- + --------- |       9*3 /   -- + ---------                              |                              9*3 /   -- + --------- |                               9*3 /   -- + --------- 
          \/    27       9                                  \                                  \/    27       9     /         \/    27       9                                  \                                \/    27       9     /                                 \/    27       9

$$\left(\frac{10}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{4}{3} + \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}\right) + \left(\left(2 + \left(- \frac{\sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2} - \frac{5}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{4}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2} + \frac{5 \sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}\right)\right)\right) + \left(- \frac{\sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2} - \frac{5}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{4}{3} + i \left(- \frac{5 \sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2}\right)\right)\right)$$

      /           ________________                          \     /             ________________                          \
      |          /          _____                           |     |            /          _____                           |
      |  ___    /  82   2*\/ 159                            |     |    ___    /  82   2*\/ 159                            |
      |\/ 3 *3 /   -- + ---------                ___        |     |  \/ 3 *3 /   -- + ---------                ___        |
      |      \/    27       9                5*\/ 3         |     |        \/    27       9                5*\/ 3         |
6 + I*|--------------------------- - -----------------------| + I*|- --------------------------- + -----------------------|
      |             2                       ________________|     |               2                       ________________|
      |                                    /          _____ |     |                                      /          _____ |
      |                                   /  82   2*\/ 159  |     |                                     /  82   2*\/ 159  |
      |                              9*3 /   -- + --------- |     |                                9*3 /   -- + --------- |
      \                                \/    27       9     /     \                                  \/    27       9     /

$$6 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2} + \frac{5 \sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}\right) + i \left(- \frac{5 \sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2}\right)$$

product

  /                                   ________________     /             ________________                          \\ /                                   ________________     /           ________________                          \\                                                      
  |                                  /          _____      |            /          _____                           || |                                  /          _____      |          /          _____                           ||                                                      
  |                                 /  82   2*\/ 159       |    ___    /  82   2*\/ 159                            || |                                 /  82   2*\/ 159       |  ___    /  82   2*\/ 159                            || /         ________________                          \
  |                              3 /   -- + ---------      |  \/ 3 *3 /   -- + ---------                ___        || |                              3 /   -- + ---------      |\/ 3 *3 /   -- + ---------                ___        || |        /          _____                           |
  |4              5              \/    27       9          |        \/    27       9                5*\/ 3         || |4              5              \/    27       9          |      \/    27       9                5*\/ 3         || |4      /  82   2*\/ 159                10          |
2*|- - ----------------------- - --------------------- + I*|- --------------------------- + -----------------------||*|- - ----------------------- - --------------------- + I*|--------------------------- - -----------------------||*|- + 3 /   -- + ---------  + -----------------------|
  |3          ________________             2               |               2                       ________________|| |3          ________________             2               |             2                       ________________|| |3   \/    27       9               ________________|
  |          /          _____                              |                                      /          _____ || |          /          _____                              |                                    /          _____ || |                                  /          _____ |
  |         /  82   2*\/ 159                               |                                     /  82   2*\/ 159  || |         /  82   2*\/ 159                               |                                   /  82   2*\/ 159  || |                                 /  82   2*\/ 159  |
  |    9*3 /   -- + ---------                              |                                9*3 /   -- + --------- || |    9*3 /   -- + ---------                              |                              9*3 /   -- + --------- || |                            9*3 /   -- + --------- |
  \      \/    27       9                                  \                                  \/    27       9     // \      \/    27       9                                  \                                \/    27       9     // \                              \/    27       9     /

$$\left(- \frac{\sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2} - \frac{5}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{4}{3} + i \left(- \frac{5 \sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2}\right)\right) 2 \left(- \frac{\sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2} - \frac{5}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{4}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2} + \frac{5 \sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}\right)\right) \left(\frac{10}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{4}{3} + \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}\right)$$

$$8$$

Rapid solution [src]

x1 = 2

$$x_{1} = 2$$

                                        ________________     /             ________________                          \
                                       /          _____      |            /          _____                           |
                                      /  82   2*\/ 159       |    ___    /  82   2*\/ 159                            |
                                   3 /   -- + ---------      |  \/ 3 *3 /   -- + ---------                ___        |
     4              5              \/    27       9          |        \/    27       9                5*\/ 3         |
x2 = - - ----------------------- - --------------------- + I*|- --------------------------- + -----------------------|
     3          ________________             2               |               2                       ________________|
               /          _____                              |                                      /          _____ |
              /  82   2*\/ 159                               |                                     /  82   2*\/ 159  |
         9*3 /   -- + ---------                              |                                9*3 /   -- + --------- |
           \/    27       9                                  \                                  \/    27       9     /

$$x_{2} = - \frac{\sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2} - \frac{5}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{4}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2} + \frac{5 \sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}\right)$$

                                        ________________     /           ________________                          \
                                       /          _____      |          /          _____                           |
                                      /  82   2*\/ 159       |  ___    /  82   2*\/ 159                            |
                                   3 /   -- + ---------      |\/ 3 *3 /   -- + ---------                ___        |
     4              5              \/    27       9          |      \/    27       9                5*\/ 3         |
x3 = - - ----------------------- - --------------------- + I*|--------------------------- - -----------------------|
     3          ________________             2               |             2                       ________________|
               /          _____                              |                                    /          _____ |
              /  82   2*\/ 159                               |                                   /  82   2*\/ 159  |
         9*3 /   -- + ---------                              |                              9*3 /   -- + --------- |
           \/    27       9                                  \                                \/    27       9     /

$$x_{3} = - \frac{\sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2} - \frac{5}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{4}{3} + i \left(- \frac{5 \sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}}{2}\right)$$

              ________________                          
             /          _____                           
     4      /  82   2*\/ 159                10          
x4 = - + 3 /   -- + ---------  + -----------------------
     3   \/    27       9               ________________
                                       /          _____ 
                                      /  82   2*\/ 159  
                                 9*3 /   -- + --------- 
                                   \/    27       9

$$x_{4} = \frac{10}{9 \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}} + \frac{4}{3} + \sqrt[3]{\frac{2 \sqrt{159}}{9} + \frac{82}{27}}$$

x4 = 10/(9*(2*sqrt(159)/9 + 82/27)^(1/3)) + 4/3 + (2*sqrt(159)/9 + 82/27)^(1/3)

Numerical answer [src]

x1 = 3.75110070237603

x2 = 0.124449648811983 + 1.02511753217493*i

x3 = 0.124449648811983 - 1.02511753217493*i

x4 = 2.0

x4 = 2.0

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Identical expressions

Similar expressions

-x^(5)+8*x^(4)-22*x^(3)+28*x^(2)-24*x+16=0 equation

Numerical solution:

The solution

-x^(5)+8x^(4)-22x^(3)+28x^(2)-24x+16=0 equation