Solve 9-3x^2x=4x^39

Question

Solve the equation

x = \frac{3 507}{13}

Alternative Form

x \approx 0.613375

Evaluate

9 - 3 x^{2} \times x = 4 x^{3} \times 9

Multiply

More Steps

Evaluate

3 x^{2} \times x

Multiply the terms with the same base by adding their exponents

3 x^{2 + 1}

Add the numbers

3 x^{3}

9 - 3 x^{3} = 4 x^{3} \times 9

Multiply the terms

9 - 3 x^{3} = 36 x^{3}

Move the expression to the left side

9 - 3 x^{3} - 36 x^{3} = 0

Subtract the terms

More Steps

Evaluate

- 3 x^{3} - 36 x^{3}

Collect like terms by calculating the sum or difference of their coefficients

(- 3 - 36) x^{3}

Subtract the numbers

- 39 x^{3}

9 - 39 x^{3} = 0

Move the constant to the right-hand side and change its sign

- 39 x^{3} = 0 - 9

Removing 0 doesn't change the value,so remove it from the expression

- 39 x^{3} = - 9

Change the signs on both sides of the equation

39 x^{3} = 9

Divide both sides

\frac{39 x ^{3}}{39} = \frac{9}{39}

Divide the numbers

x^{3} = \frac{9}{39}

Cancel out the common factor 3

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

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

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

Calculate

x = 3 \frac{3}{13}

Solution

More Steps

Evaluate

3 \frac{3}{13}

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

\frac{3 3}{3 13}

Multiply by the Conjugate

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

Simplify

\frac{3 3 \times 3 169}{3 13 \times 3 1 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3169

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

3 3 \times 169

Calculate the product

3507

\frac{3 507}{3 13 \times 3 1 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 3 1 3^{2}

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

3 13 \times 1 3^{2}

Calculate the product

3 1 3^{3}

Reduce the index of the radical and exponent with 3

13

\frac{3 507}{13}

x = \frac{3 507}{13}

Alternative Form

x \approx 0.613375

Show Solution