Solve 3(x 7)*x^3=18

Question

3 (x \times 7) x^{3} = 18

Solve the equation

x_{1} = - \frac{4 2058}{7}, x_{2} = \frac{4 2058}{7}

Alternative Form

x_{1} \approx - 0.962195, x_{2} \approx 0.962195

Evaluate

3 (x \times 7) x^{3} = 18

Remove the parentheses

3 x \times 7 x^{3} = 18

Multiply

More Steps

Evaluate

3 x \times 7 x^{3}

Multiply the terms

21 x \times x^{3}

Multiply the terms with the same base by adding their exponents

21 x^{1 + 3}

Add the numbers

21 x^{4}

21 x^{4} = 18

Divide both sides

\frac{21 x ^{4}}{21} = \frac{18}{21}

Divide the numbers

x^{4} = \frac{18}{21}

Cancel out the common factor 3

x^{4} = \frac{6}{7}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{6}{7}

Simplify the expression

More Steps

Evaluate

4 \frac{6}{7}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 6}{4 7}

Multiply by the Conjugate

\frac{4 6 \times 4 7 ^{3}}{4 7 \times 4 7 ^{3}}

Simplify

\frac{4 6 \times 4 343}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

46 \times 4343

The product of roots with the same index is equal to the root of the product

4 6 \times 343

Calculate the product

42058

\frac{4 2058}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

47 \times 4 7^{3}

The product of roots with the same index is equal to the root of the product

4 7 \times 7^{3}

Calculate the product

4 7^{4}

Reduce the index of the radical and exponent with 4

7

\frac{4 2058}{7}

x = \pm \frac{4 2058}{7}

Separate the equation into 2 possible cases

x = \frac{4 2058}{7} x = - \frac{4 2058}{7}

Solution

x_{1} = - \frac{4 2058}{7}, x_{2} = \frac{4 2058}{7}

Alternative Form

x_{1} \approx - 0.962195, x_{2} \approx 0.962195

Show Solution