Solve x 12x^23x^3=19

Question

Solve the equation

x_{1} = - \frac{6 24624}{6}, x_{2} = \frac{6 24624}{6}

Alternative Form

x_{1} \approx - 0.898963, x_{2} \approx 0.898963

Evaluate

x \times 12 x^{2} \times 3 x^{3} = 19

Multiply

More Steps

Evaluate

x \times 12 x^{2} \times 3 x^{3}

Multiply the terms with the same base by adding their exponents

x^{1 + 2 + 3} \times 12 \times 3

Add the numbers

x^{6} \times 12 \times 3

Multiply the terms

x^{6} \times 36

Use the commutative property to reorder the terms

36 x^{6}

36 x^{6} = 19

Divide both sides

\frac{36 x ^{6}}{36} = \frac{19}{36}

Divide the numbers

x^{6} = \frac{19}{36}

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

x = \pm 6 \frac{19}{36}

Simplify the expression

More Steps

Evaluate

6 \frac{19}{36}

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

\frac{6 19}{6 36}

Simplify the radical expression

\frac{6 19}{3 6}

Multiply by the Conjugate

\frac{6 19 \times 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{6 19 \times 3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

619 \times 336

Use n a = mn a^{m} to expand the expression

619 \times 6 3 6^{2}

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

6 19 \times 3 6^{2}

Calculate the product

624624

\frac{6 24624}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 3 6^{2}

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

3 6 \times 6^{2}

Calculate the product

3 6^{3}

Reduce the index of the radical and exponent with 3

6

\frac{6 24624}{6}

x = \pm \frac{6 24624}{6}

Separate the equation into 2 possible cases

x = \frac{6 24624}{6} x = - \frac{6 24624}{6}

Solution

x_{1} = - \frac{6 24624}{6}, x_{2} = \frac{6 24624}{6}

Alternative Form

x_{1} \approx - 0.898963, x_{2} \approx 0.898963

Show Solution