Solve 32x=5x^3 - ScanMath

Question

Solve the equation

x_{1} = - \frac{4 10}{5}, x_{2} = 0, x_{3} = \frac{4 10}{5}

Alternative Form

x_{1} \approx - 2.529822, x_{2} = 0, x_{3} \approx 2.529822

Evaluate

32 x = 5 x^{3}

Add or subtract both sides

32 x - 5 x^{3} = 0

Factor the expression

x (32 - 5 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 32 - 5 x^{2} = 0

Solve the equation

More Steps

Evaluate

32 - 5 x^{2} = 0

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

- 5 x^{2} = 0 - 32

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

- 5 x^{2} = - 32

Change the signs on both sides of the equation

5 x^{2} = 32

Divide both sides

\frac{5 x ^{2}}{5} = \frac{32}{5}

Divide the numbers

x^{2} = \frac{32}{5}

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

x = \pm \frac{32}{5}

Simplify the expression

More Steps

Evaluate

\frac{32}{5}

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

\frac{32}{5}

Simplify the radical expression

\frac{4 2}{5}

Multiply by the Conjugate

\frac{4 2 \times 5}{5 \times 5}

Multiply the numbers

\frac{4 10}{5 \times 5}

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

\frac{4 10}{5}

x = \pm \frac{4 10}{5}

Separate the equation into 2 possible cases

x = \frac{4 10}{5} x = - \frac{4 10}{5}

x = 0 x = \frac{4 10}{5} x = - \frac{4 10}{5}

Solution

x_{1} = - \frac{4 10}{5}, x_{2} = 0, x_{3} = \frac{4 10}{5}

Alternative Form

x_{1} \approx - 2.529822, x_{2} = 0, x_{3} \approx 2.529822

Show Solution