Solve x 1=3x^3 - ScanMath

Question

Solve the equation

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

Alternative Form

x_{1} \approx - 0.57735, x_{2} = 0, x_{3} \approx 0.57735

Evaluate

x \times 1 = 3 x^{3}

Any expression multiplied by 1 remains the same

x = 3 x^{3}

Add or subtract both sides

x - 3 x^{3} = 0

Factor the expression

x (1 - 3 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 1 - 3 x^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 3 x^{2} = 0

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

- 3 x^{2} = 0 - 1

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

- 3 x^{2} = - 1

Change the signs on both sides of the equation

3 x^{2} = 1

Divide both sides

\frac{3 x ^{2}}{3} = \frac{1}{3}

Divide the numbers

x^{2} = \frac{1}{3}

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

x = \pm \frac{1}{3}

Simplify the expression

More Steps

Evaluate

\frac{1}{3}

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

\frac{1}{3}

Simplify the radical expression

\frac{1}{3}

Multiply by the Conjugate

\frac{3}{3 \times 3}

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

\frac{3}{3}

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

Separate the equation into 2 possible cases

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

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

Solution

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

Alternative Form

x_{1} \approx - 0.57735, x_{2} = 0, x_{3} \approx 0.57735

Show Solution