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Equation:
Equation x^2=12
Equation 3^x=81
Equation x^2-8x+12=0
Equation x^6=-(12-8x)^3
Express {x} in terms of y where:
-5*x-6*y=-1
1*x+6*y=-6
-5*x+6*y=-8
-2*x-9*y=10
Graphing y =:
x^6
Integral of d{x}:
x^6
Derivative of:
x^6
Identical expressions
x^ six =-(twelve -8x)^ three
x to the power of 6 equally minus (12 minus 8x) cubed
x to the power of six equally minus (twelve minus 8x) to the power of three
x6=-(12-8x)3
x6=-12-8x3
x⁶=-(12-8x)³
x to the power of 6=-(12-8x) to the power of 3
x^6=-12-8x^3
Similar expressions
x^6=-(12+8x)^3
x^6=+(12-8x)^3

x^6=-(12-8x)^3 equation

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

The solution

You have entered [src]

 6              3
x  = -(12 - 8*x)

$$x^{6} = - \left(12 - 8 x\right)^{3}$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

x1 = 2

$$x_{1} = 2$$

x2 = 6

$$x_{2} = 6$$

            /                        /    /    ___\\\               /    /    ___\\
            |      ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|
x3 = -2 + I*|- 2*\/ 3  + 2*\/ 37 *cos|-------------|| + 2*\/ 37 *sin|-------------|
            \                        \      2      //               \      2      /

$$x_{3} = -2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)$$

            /                      /    /    ___\\\               /    /    ___\\
            |    ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|
x4 = -2 + I*|2*\/ 3  + 2*\/ 37 *cos|-------------|| - 2*\/ 37 *sin|-------------|
            \                      \      2      //               \      2      /

$$x_{4} = - 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)$$

            /                      /    /    ___\\\               /    /    ___\\
            |    ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|
x5 = -2 + I*|2*\/ 3  - 2*\/ 37 *cos|-------------|| + 2*\/ 37 *sin|-------------|
            \                      \      2      //               \      2      /

$$x_{5} = -2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + 2 \sqrt{3}\right)$$

            /                        /    /    ___\\\               /    /    ___\\
            |      ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|
x6 = -2 + I*|- 2*\/ 3  - 2*\/ 37 *cos|-------------|| - 2*\/ 37 *sin|-------------|
            \                        \      2      //               \      2      /

$$x_{6} = - 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 \sqrt{3}\right)$$

x6 = -2*37^(1/4)*sin(atan(7*sqrt(3))/2) - 2 + i*(-2*37^(1/4)*cos(atan(7*sqrt(3))/2) - 2*sqrt(3))

Sum and product of roots [src]

sum

               /                        /    /    ___\\\               /    /    ___\\          /                      /    /    ___\\\               /    /    ___\\          /                      /    /    ___\\\               /    /    ___\\          /                        /    /    ___\\\               /    /    ___\\
               |      ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|          |    ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|          |    ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|          |      ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|
2 + 6 + -2 + I*|- 2*\/ 3  + 2*\/ 37 *cos|-------------|| + 2*\/ 37 *sin|-------------| + -2 + I*|2*\/ 3  + 2*\/ 37 *cos|-------------|| - 2*\/ 37 *sin|-------------| + -2 + I*|2*\/ 3  - 2*\/ 37 *cos|-------------|| + 2*\/ 37 *sin|-------------| + -2 + I*|- 2*\/ 3  - 2*\/ 37 *cos|-------------|| - 2*\/ 37 *sin|-------------|
               \                        \      2      //               \      2      /          \                      \      2      //               \      2      /          \                      \      2      //               \      2      /          \                        \      2      //               \      2      /

$$\left(- 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 \sqrt{3}\right)\right) + \left(\left(-2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + 2 \sqrt{3}\right)\right) + \left(\left(\left(2 + 6\right) + \left(-2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right)\right) + \left(- 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right)\right)\right)$$

  /                        /    /    ___\\\     /                        /    /    ___\\\     /                      /    /    ___\\\     /                      /    /    ___\\\
  |      ___     4 ____    |atan\7*\/ 3 /||     |      ___     4 ____    |atan\7*\/ 3 /||     |    ___     4 ____    |atan\7*\/ 3 /||     |    ___     4 ____    |atan\7*\/ 3 /||
I*|- 2*\/ 3  - 2*\/ 37 *cos|-------------|| + I*|- 2*\/ 3  + 2*\/ 37 *cos|-------------|| + I*|2*\/ 3  - 2*\/ 37 *cos|-------------|| + I*|2*\/ 3  + 2*\/ 37 *cos|-------------||
  \                        \      2      //     \                        \      2      //     \                      \      2      //     \                      \      2      //

$$i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 \sqrt{3}\right) + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + 2 \sqrt{3}\right) + i \left(- 2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right) + i \left(2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)$$

product

    /       /                        /    /    ___\\\               /    /    ___\\\ /       /                      /    /    ___\\\               /    /    ___\\\ /       /                      /    /    ___\\\               /    /    ___\\\ /       /                        /    /    ___\\\               /    /    ___\\\
    |       |      ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|| |       |    ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|| |       |    ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|| |       |      ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /||
2*6*|-2 + I*|- 2*\/ 3  + 2*\/ 37 *cos|-------------|| + 2*\/ 37 *sin|-------------||*|-2 + I*|2*\/ 3  + 2*\/ 37 *cos|-------------|| - 2*\/ 37 *sin|-------------||*|-2 + I*|2*\/ 3  - 2*\/ 37 *cos|-------------|| + 2*\/ 37 *sin|-------------||*|-2 + I*|- 2*\/ 3  - 2*\/ 37 *cos|-------------|| - 2*\/ 37 *sin|-------------||
    \       \                        \      2      //               \      2      // \       \                      \      2      //               \      2      // \       \                      \      2      //               \      2      // \       \                        \      2      //               \      2      //

$$2 \cdot 6 \left(-2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right) \left(- 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right) \left(-2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + 2 \sqrt{3}\right)\right) \left(- 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 \sqrt{3}\right)\right)$$

$$1728$$

Numerical answer [src]

x1 = 6.0

x2 = 1.34148545718763 - 0.164331250521529*i

x3 = 2.0

x4 = -5.34148545718763 - 7.09253448079704*i

x5 = -5.34148545718763 + 7.09253448079704*i

x6 = 1.34148545718763 + 0.164331250521529*i

x6 = 1.34148545718763 + 0.164331250521529*i

The graph

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x^6=-(12-8x)^3 equation

Numerical solution:

The solution