Solve 1000x^3-10x

Question

Factor the expression

10 x (10 x - 1) (10 x + 1)

Evaluate

1000 x^{3} - 10 x

Factor out 10 x from the expression

10 x (100 x^{2} - 1)

Solution

More Steps

Evaluate

100 x^{2} - 1

Rewrite the expression in exponential form

(10 x)^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(10 x - 1) (10 x + 1)

10 x (10 x - 1) (10 x + 1)

Show Solution

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

Alternative Form

x_{1} = - 0.1, x_{2} = 0, x_{3} = 0.1

Evaluate

1000 x^{3} - 10 x

To find the roots of the expression,set the expression equal to 0

1000 x^{3} - 10 x = 0

Factor the expression

10 x (100 x^{2} - 1) = 0

Divide both sides

x (100 x^{2} - 1) = 0

Separate the equation into 2 possible cases

x = 0 100 x^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

100 x^{2} - 1 = 0

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

100 x^{2} = 0 + 1

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

100 x^{2} = 1

Divide both sides

\frac{100 x ^{2}}{100} = \frac{1}{100}

Divide the numbers

x^{2} = \frac{1}{100}

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

x = \pm \frac{1}{100}

Simplify the expression

More Steps

Evaluate

\frac{1}{100}

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

\frac{1}{100}

Simplify the radical expression

\frac{1}{100}

Simplify the radical expression

\frac{1}{10}

x = \pm \frac{1}{10}

Separate the equation into 2 possible cases

x = \frac{1}{10} x = - \frac{1}{10}

x = 0 x = \frac{1}{10} x = - \frac{1}{10}

Solution

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

Alternative Form

x_{1} = - 0.1, x_{2} = 0, x_{3} = 0.1

Show Solution