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x^6=-(7x+10)^3

x^6=-(7x+10)^3 equation

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Numerical solution:

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The solution

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 6              3
x  = -(7*x + 10)
x6=−(7x+10)3x^{6} = - \left(7 x + 10\right)^{3}
Simplify
The graph
80246-14-12-10-8-6-4-220000000-10000000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -5
x1=−5x_{1} = -5 
x2 = -2
x2=−2x_{2} = -2 
           /                        /    /     ___\\\               /    /     ___\\
           |                        |    |89*\/ 3 |||               |    |89*\/ 3 ||
           |                        |atan|--------|||               |atan|--------||
           |            4 ______    |    \   9    /||   4 ______    |    \   9    /|
           |      ___   \/ 5961 *cos|--------------||   \/ 5961 *sin|--------------|
     7     |  7*\/ 3                \      2       /|               \      2       /
x3 = - + I*|- ------- + ----------------------------| - ----------------------------
     4     \     4                   2              /                2
x3=−59614sin⁡(atan⁡(8939)2)2+74+i(−734+59614cos⁡(atan⁡(8939)2)2)x_{3} = - \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7}{4} + i \left(- \frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right) 
           /                      /    /     ___\\\               /    /     ___\\
           |                      |    |89*\/ 3 |||               |    |89*\/ 3 ||
           |                      |atan|--------|||               |atan|--------||
           |          4 ______    |    \   9    /||   4 ______    |    \   9    /|
           |    ___   \/ 5961 *cos|--------------||   \/ 5961 *sin|--------------|
     7     |7*\/ 3                \      2       /|               \      2       /
x4 = - + I*|------- + ----------------------------| + ----------------------------
     4     \   4                   2              /                2
x4=74+59614sin⁡(atan⁡(8939)2)2+i(734+59614cos⁡(atan⁡(8939)2)2)x_{4} = \frac{7}{4} + \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(\frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right) 
           /                        /    /     ___\\\               /    /     ___\\
           |                        |    |89*\/ 3 |||               |    |89*\/ 3 ||
           |                        |atan|--------|||               |atan|--------||
           |            4 ______    |    \   9    /||   4 ______    |    \   9    /|
           |      ___   \/ 5961 *cos|--------------||   \/ 5961 *sin|--------------|
     7     |  7*\/ 3                \      2       /|               \      2       /
x5 = - + I*|- ------- - ----------------------------| + ----------------------------
     4     \     4                   2              /                2
x5=74+59614sin⁡(atan⁡(8939)2)2+i(−59614cos⁡(atan⁡(8939)2)2−734)x_{5} = \frac{7}{4} + \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{7 \sqrt{3}}{4}\right) 
           /                      /    /     ___\\\               /    /     ___\\
           |                      |    |89*\/ 3 |||               |    |89*\/ 3 ||
           |                      |atan|--------|||               |atan|--------||
           |          4 ______    |    \   9    /||   4 ______    |    \   9    /|
           |    ___   \/ 5961 *cos|--------------||   \/ 5961 *sin|--------------|
     7     |7*\/ 3                \      2       /|               \      2       /
x6 = - + I*|------- - ----------------------------| - ----------------------------
     4     \   4                   2              /                2
x6=−59614sin⁡(atan⁡(8939)2)2+74+i(−59614cos⁡(atan⁡(8939)2)2+734)x_{6} = - \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7}{4} + i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7 \sqrt{3}}{4}\right) 
x6 = -5961^(1/4)*sin(atan(89*sqrt(3)/9)/2)/2 + 7/4 + i*(-5961^(1/4)*cos(atan(89*sqrt(3)/9)/2)/2 + 7*sqrt(3)/4)
Sum and product of roots [src] 
sum
               /                        /    /     ___\\\               /    /     ___\\         /                      /    /     ___\\\               /    /     ___\\         /                        /    /     ___\\\               /    /     ___\\         /                      /    /     ___\\\               /    /     ___\\
               |                        |    |89*\/ 3 |||               |    |89*\/ 3 ||         |                      |    |89*\/ 3 |||               |    |89*\/ 3 ||         |                        |    |89*\/ 3 |||               |    |89*\/ 3 ||         |                      |    |89*\/ 3 |||               |    |89*\/ 3 ||
               |                        |atan|--------|||               |atan|--------||         |                      |atan|--------|||               |atan|--------||         |                        |atan|--------|||               |atan|--------||         |                      |atan|--------|||               |atan|--------||
               |            4 ______    |    \   9    /||   4 ______    |    \   9    /|         |          4 ______    |    \   9    /||   4 ______    |    \   9    /|         |            4 ______    |    \   9    /||   4 ______    |    \   9    /|         |          4 ______    |    \   9    /||   4 ______    |    \   9    /|
               |      ___   \/ 5961 *cos|--------------||   \/ 5961 *sin|--------------|         |    ___   \/ 5961 *cos|--------------||   \/ 5961 *sin|--------------|         |      ___   \/ 5961 *cos|--------------||   \/ 5961 *sin|--------------|         |    ___   \/ 5961 *cos|--------------||   \/ 5961 *sin|--------------|
         7     |  7*\/ 3                \      2       /|               \      2       /   7     |7*\/ 3                \      2       /|               \      2       /   7     |  7*\/ 3                \      2       /|               \      2       /   7     |7*\/ 3                \      2       /|               \      2       /
-5 - 2 + - + I*|- ------- + ----------------------------| - ---------------------------- + - + I*|------- + ----------------------------| + ---------------------------- + - + I*|- ------- - ----------------------------| + ---------------------------- + - + I*|------- - ----------------------------| - ----------------------------
         4     \     4                   2              /                2                 4     \   4                   2              /                2                 4     \     4                   2              /                2                 4     \   4                   2              /                2
(−59614sin⁡(atan⁡(8939)2)2+74+i(−59614cos⁡(atan⁡(8939)2)2+734))+((74+59614sin⁡(atan⁡(8939)2)2+i(−59614cos⁡(atan⁡(8939)2)2−734))+(((−5−2)+(−59614sin⁡(atan⁡(8939)2)2+74+i(−734+59614cos⁡(atan⁡(8939)2)2)))+(74+59614sin⁡(atan⁡(8939)2)2+i(734+59614cos⁡(atan⁡(8939)2)2))))\left(- \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7}{4} + i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7 \sqrt{3}}{4}\right)\right) + \left(\left(\frac{7}{4} + \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{7 \sqrt{3}}{4}\right)\right) + \left(\left(\left(-5 - 2\right) + \left(- \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7}{4} + i \left(- \frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)\right)\right) + \left(\frac{7}{4} + \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(\frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)\right)\right)\right) 
=
  /                        /    /     ___\\\     /                        /    /     ___\\\     /                      /    /     ___\\\     /                      /    /     ___\\\
  |                        |    |89*\/ 3 |||     |                        |    |89*\/ 3 |||     |                      |    |89*\/ 3 |||     |                      |    |89*\/ 3 |||
  |                        |atan|--------|||     |                        |atan|--------|||     |                      |atan|--------|||     |                      |atan|--------|||
  |            4 ______    |    \   9    /||     |            4 ______    |    \   9    /||     |          4 ______    |    \   9    /||     |          4 ______    |    \   9    /||
  |      ___   \/ 5961 *cos|--------------||     |      ___   \/ 5961 *cos|--------------||     |    ___   \/ 5961 *cos|--------------||     |    ___   \/ 5961 *cos|--------------||
  |  7*\/ 3                \      2       /|     |  7*\/ 3                \      2       /|     |7*\/ 3                \      2       /|     |7*\/ 3                \      2       /|
I*|- ------- + ----------------------------| + I*|- ------- - ----------------------------| + I*|------- + ----------------------------| + I*|------- - ----------------------------|
  \     4                   2              /     \     4                   2              /     \   4                   2              /     \   4                   2              /
i(−59614cos⁡(atan⁡(8939)2)2−734)+i(−59614cos⁡(atan⁡(8939)2)2+734)+i(−734+59614cos⁡(atan⁡(8939)2)2)+i(734+59614cos⁡(atan⁡(8939)2)2)i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{7 \sqrt{3}}{4}\right) + i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7 \sqrt{3}}{4}\right) + i \left(- \frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right) + i \left(\frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right) 
product
        /      /                        /    /     ___\\\               /    /     ___\\\ /      /                      /    /     ___\\\               /    /     ___\\\ /      /                        /    /     ___\\\               /    /     ___\\\ /      /                      /    /     ___\\\               /    /     ___\\\
        |      |                        |    |89*\/ 3 |||               |    |89*\/ 3 ||| |      |                      |    |89*\/ 3 |||               |    |89*\/ 3 ||| |      |                        |    |89*\/ 3 |||               |    |89*\/ 3 ||| |      |                      |    |89*\/ 3 |||               |    |89*\/ 3 |||
        |      |                        |atan|--------|||               |atan|--------||| |      |                      |atan|--------|||               |atan|--------||| |      |                        |atan|--------|||               |atan|--------||| |      |                      |atan|--------|||               |atan|--------|||
        |      |            4 ______    |    \   9    /||   4 ______    |    \   9    /|| |      |          4 ______    |    \   9    /||   4 ______    |    \   9    /|| |      |            4 ______    |    \   9    /||   4 ______    |    \   9    /|| |      |          4 ______    |    \   9    /||   4 ______    |    \   9    /||
        |      |      ___   \/ 5961 *cos|--------------||   \/ 5961 *sin|--------------|| |      |    ___   \/ 5961 *cos|--------------||   \/ 5961 *sin|--------------|| |      |      ___   \/ 5961 *cos|--------------||   \/ 5961 *sin|--------------|| |      |    ___   \/ 5961 *cos|--------------||   \/ 5961 *sin|--------------||
        |7     |  7*\/ 3                \      2       /|               \      2       /| |7     |7*\/ 3                \      2       /|               \      2       /| |7     |  7*\/ 3                \      2       /|               \      2       /| |7     |7*\/ 3                \      2       /|               \      2       /|
-5*(-2)*|- + I*|- ------- + ----------------------------| - ----------------------------|*|- + I*|------- + ----------------------------| + ----------------------------|*|- + I*|- ------- - ----------------------------| + ----------------------------|*|- + I*|------- - ----------------------------| - ----------------------------|
        \4     \     4                   2              /                2              / \4     \   4                   2              /                2              / \4     \     4                   2              /                2              / \4     \   4                   2              /                2              /
−−10(−59614sin⁡(atan⁡(8939)2)2+74+i(−734+59614cos⁡(atan⁡(8939)2)2))(74+59614sin⁡(atan⁡(8939)2)2+i(734+59614cos⁡(atan⁡(8939)2)2))(74+59614sin⁡(atan⁡(8939)2)2+i(−59614cos⁡(atan⁡(8939)2)2−734))(−59614sin⁡(atan⁡(8939)2)2+74+i(−59614cos⁡(atan⁡(8939)2)2+734))- -10 \left(- \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7}{4} + i \left(- \frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)\right) \left(\frac{7}{4} + \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(\frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)\right) \left(\frac{7}{4} + \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{7 \sqrt{3}}{4}\right)\right) \left(- \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7}{4} + i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7 \sqrt{3}}{4}\right)\right) 
=
1000
10001000 
1000
Numerical answer [src] 
x1 = -2.0
x2 = -1.26470381189907 - 0.164758247286208*i
x3 = -1.26470381189907 + 0.164758247286208*i
x4 = 4.76470381189907 - 6.22693607377728*i
x5 = 4.76470381189907 + 6.22693607377728*i
x6 = -5.0
x6 = -5.0
The graph
x^6=-(7x+10)^3 equation
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