Solve 180 = 3x^322x 1

Question

Solve the equation

x_{1} = - \frac{4 39930}{11}, x_{2} = \frac{4 39930}{11}

Alternative Form

x_{1} \approx - 1.285086, x_{2} \approx 1.285086

Evaluate

180 = 3 x^{3} \times 22 x \times 1

Multiply the terms

More Steps

Evaluate

3 x^{3} \times 22 x \times 1

Rewrite the expression

3 x^{3} \times 22 x

Multiply the terms

66 x^{3} \times x

Multiply the terms with the same base by adding their exponents

66 x^{3 + 1}

Add the numbers

66 x^{4}

180 = 66 x^{4}

Swap the sides of the equation

66 x^{4} = 180

Divide both sides

\frac{66 x ^{4}}{66} = \frac{180}{66}

Divide the numbers

x^{4} = \frac{180}{66}

Cancel out the common factor 6

x^{4} = \frac{30}{11}

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

x = \pm 4 \frac{30}{11}

Simplify the expression

More Steps

Evaluate

4 \frac{30}{11}

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

\frac{4 30}{4 11}

Multiply by the Conjugate

\frac{4 30 \times 4 1 1 ^{3}}{4 11 \times 4 1 1 ^{3}}

Simplify

\frac{4 30 \times 4 1331}{4 11 \times 4 1 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

430 \times 41331

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

4 30 \times 1331

Calculate the product

439930

\frac{4 39930}{4 11 \times 4 1 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

411 \times 4 1 1^{3}

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

4 11 \times 1 1^{3}

Calculate the product

4 1 1^{4}

Reduce the index of the radical and exponent with 4

11

\frac{4 39930}{11}

x = \pm \frac{4 39930}{11}

Separate the equation into 2 possible cases

x = \frac{4 39930}{11} x = - \frac{4 39930}{11}

Solution

x_{1} = - \frac{4 39930}{11}, x_{2} = \frac{4 39930}{11}

Alternative Form

x_{1} \approx - 1.285086, x_{2} \approx 1.285086

Show Solution