Solve 5(x^3)=3(x 9)

Question

Solve the equation

x_{1} = - \frac{3 15}{5}, x_{2} = 0, x_{3} = \frac{3 15}{5}

Alternative Form

x_{1} \approx - 2.32379, x_{2} = 0, x_{3} \approx 2.32379

Evaluate

5 x^{3} = 3 (x \times 9)

Remove the parentheses

5 x^{3} = 3 x \times 9

Multiply the terms

5 x^{3} = 27 x

Add or subtract both sides

5 x^{3} - 27 x = 0

Factor the expression

x (5 x^{2} - 27) = 0

Separate the equation into 2 possible cases

x = 0 5 x^{2} - 27 = 0

Solve the equation

More Steps

Evaluate

5 x^{2} - 27 = 0

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

5 x^{2} = 0 + 27

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

5 x^{2} = 27

Divide both sides

\frac{5 x ^{2}}{5} = \frac{27}{5}

Divide the numbers

x^{2} = \frac{27}{5}

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

x = \pm \frac{27}{5}

Simplify the expression

More Steps

Evaluate

\frac{27}{5}

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

\frac{27}{5}

Simplify the radical expression

\frac{3 3}{5}

Multiply by the Conjugate

\frac{3 3 \times 5}{5 \times 5}

Multiply the numbers

\frac{3 15}{5 \times 5}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{3 15}{5}

x = \pm \frac{3 15}{5}

Separate the equation into 2 possible cases

x = \frac{3 15}{5} x = - \frac{3 15}{5}

x = 0 x = \frac{3 15}{5} x = - \frac{3 15}{5}

Solution

x_{1} = - \frac{3 15}{5}, x_{2} = 0, x_{3} = \frac{3 15}{5}

Alternative Form

x_{1} \approx - 2.32379, x_{2} = 0, x_{3} \approx 2.32379

Show Solution