Solve x^3=38808*7*3/4*22

$$x ^ { 3 } = \frac { 38808 \times 7 \times 3 } { 4 \times 22 }$$

Solve for x (complex solution)

$$x=\frac{-21\sqrt{3}i-21}{2}\approx -10.5-18.186533479i$$

$$x=21$$

$$x=\frac{-21+21\sqrt{3}i}{2}\approx -10.5+18.186533479i$$

Solution Steps

Cancel out 4\times 22 in both numerator and denominator.

$$x^{3}=3\times 7\times 441$$

Multiply 3 and 7 to get 21.

$$x^{3}=21\times 441$$

Multiply 21 and 441 to get 9261.

$$x^{3}=9261$$

Subtract 9261 from both sides.

$$x^{3}-9261=0$$

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -9261 and q divides the leading coefficient 1. List all candidates \frac{p}{q}.

$$±9261,±3087,±1323,±1029,±441,±343,±189,±147,±63,±49,±27,±21,±9,±7,±3,±1$$

Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

$$x=21$$

By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x^{3}-9261 by x-21 to get x^{2}+21x+441. Solve the equation where the result equals to 0.

$$x^{2}+21x+441=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, 21 for b, and 441 for c in the quadratic formula.

$$x=\frac{-21±\sqrt{21^{2}-4\times 1\times 441}}{2}$$

Do the calculations.

$$x=\frac{-21±\sqrt{-1323}}{2}$$

Solve the equation x^{2}+21x+441=0 when ± is plus and when ± is minus.

$$x=\frac{-21i\sqrt{3}-21}{2} x=\frac{-21+21i\sqrt{3}}{2}$$

List all found solutions.

$$x=21 x=\frac{-21i\sqrt{3}-21}{2} x=\frac{-21+21i\sqrt{3}}{2}$$

Solve for x

$$x=21$$

Solution Steps

Cancel out 4\times 22 in both numerator and denominator.

$$x^{3}=3\times 7\times 441$$

Multiply 3 and 7 to get 21.

$$x^{3}=21\times 441$$

Multiply 21 and 441 to get 9261.

$$x^{3}=9261$$

Subtract 9261 from both sides.

$$x^{3}-9261=0$$

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -9261 and q divides the leading coefficient 1. List all candidates \frac{p}{q}.

$$±9261,±3087,±1323,±1029,±441,±343,±189,±147,±63,±49,±27,±21,±9,±7,±3,±1$$

Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

$$x=21$$

By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x^{3}-9261 by x-21 to get x^{2}+21x+441. Solve the equation where the result equals to 0.

$$x^{2}+21x+441=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, 21 for b, and 441 for c in the quadratic formula.

$$x=\frac{-21±\sqrt{21^{2}-4\times 1\times 441}}{2}$$

Do the calculations.

$$x=\frac{-21±\sqrt{-1323}}{2}$$

Since the square root of a negative number is not defined in the real field, there are no solutions.

$$x\in \emptyset$$

List all found solutions.

$$x=21$$