Solve 14x^3/2=x 9

Question

Solve the equation

x_{1} = - \frac{3 7}{7}, x_{2} = 0, x_{3} = \frac{3 7}{7}

Alternative Form

x_{1} \approx - 1.133893, x_{2} = 0, x_{3} \approx 1.133893

Evaluate

14 \times \frac{x ^{3}}{2} = x \times 9

Cancel out the common factor 2

7 x^{3} = x \times 9

Use the commutative property to reorder the terms

7 x^{3} = 9 x

Add or subtract both sides

7 x^{3} - 9 x = 0

Factor the expression

x (7 x^{2} - 9) = 0

Separate the equation into 2 possible cases

x = 0 7 x^{2} - 9 = 0

Solve the equation

More Steps

Evaluate

7 x^{2} - 9 = 0

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

7 x^{2} = 0 + 9

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

7 x^{2} = 9

Divide both sides

\frac{7 x ^{2}}{7} = \frac{9}{7}

Divide the numbers

x^{2} = \frac{9}{7}

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

x = \pm \frac{9}{7}

Simplify the expression

More Steps

Evaluate

\frac{9}{7}

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

\frac{9}{7}

Simplify the radical expression

\frac{3}{7}

Multiply by the Conjugate

\frac{3 7}{7 \times 7}

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

\frac{3 7}{7}

x = \pm \frac{3 7}{7}

Separate the equation into 2 possible cases

x = \frac{3 7}{7} x = - \frac{3 7}{7}

x = 0 x = \frac{3 7}{7} x = - \frac{3 7}{7}

Solution

x_{1} = - \frac{3 7}{7}, x_{2} = 0, x_{3} = \frac{3 7}{7}

Alternative Form

x_{1} \approx - 1.133893, x_{2} = 0, x_{3} \approx 1.133893

Show Solution