Solve x^2 13/3x=56/36

Question

Solve the equation

x = \frac{3 21294}{39}

Alternative Form

x \approx 0.710702

Evaluate

x^{2} \times \frac{13}{3} x = \frac{56}{36}

Multiply

More Steps

Evaluate

x^{2} \times \frac{13}{3} x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times \frac{13}{3}

Add the numbers

x^{3} \times \frac{13}{3}

Use the commutative property to reorder the terms

\frac{13}{3} x^{3}

\frac{13}{3} x^{3} = \frac{56}{36}

Cancel out the common factor 4

\frac{13}{3} x^{3} = \frac{14}{9}

Multiply by the reciprocal

\frac{13}{3} x^{3} \times \frac{3}{13} = \frac{14}{9} \times \frac{3}{13}

Multiply

x^{3} = \frac{14}{9} \times \frac{3}{13}

Multiply

More Steps

Evaluate

\frac{14}{9} \times \frac{3}{13}

Reduce the numbers

\frac{14}{3} \times \frac{1}{13}

To multiply the fractions,multiply the numerators and denominators separately

\frac{14}{3 \times 13}

Multiply the numbers

\frac{14}{39}

x^{3} = \frac{14}{39}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{14}{39}

Calculate

x = 3 \frac{14}{39}

Solution

More Steps

Evaluate

3 \frac{14}{39}

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

\frac{3 14}{3 39}

Multiply by the Conjugate

\frac{3 14 \times 3 3 9 ^{2}}{3 39 \times 3 3 9 ^{2}}

Simplify

\frac{3 14 \times 3 1521}{3 39 \times 3 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

314 \times 31521

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

3 14 \times 1521

Calculate the product

321294

\frac{3 21294}{3 39 \times 3 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

339 \times 3 3 9^{2}

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

3 39 \times 3 9^{2}

Calculate the product

3 3 9^{3}

Reduce the index of the radical and exponent with 3

39

\frac{3 21294}{39}

x = \frac{3 21294}{39}

Alternative Form

x \approx 0.710702

Show Solution