Solve x^2 10x<=-21

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \leq - \frac{3 2100}{10}

Alternative Form

x \in (- \infty, - \frac{3 2100}{10}]

Evaluate

x^{2} \times 10 x \leq - 21

Multiply

More Steps

10 x^{3} \leq - 21

Move the expression to the left side

10 x^{3} - (- 21) \leq 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

10 x^{3} + 21 \leq 0

Rewrite the expression

10 x^{3} + 21 = 0

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

10 x^{3} = 0 - 21

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

10 x^{3} = - 21

Divide both sides

\frac{10 x ^{3}}{10} = \frac{- 21}{10}

Divide the numbers

x^{3} = \frac{- 21}{10}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{3} = - \frac{21}{10}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{21}{10}

Calculate

x = 3 - \frac{21}{10}

Simplify the root

More Steps

x = - \frac{3 2100}{10}

Determine the test intervals using the critical values

x < - \frac{3 2100}{10} x > - \frac{3 2100}{10}

Choose a value form each interval

x_{1} = - 2 x_{2} = 0

To determine if x < - \frac{3 2100}{10} is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - \frac{3 2100}{10} is the solution x_{2} = 0

To determine if x > - \frac{3 2100}{10} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - \frac{3 2100}{10} is the solution x > - \frac{3 2100}{10} is not a solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

x \leq - \frac{3 2100}{10} is the solution

Solution

x \leq - \frac{3 2100}{10}

Alternative Form

x \in (- \infty, - \frac{3 2100}{10}]

Show Solution