Solve x^(2) x-6≥0

Evaluate

x^{2} \times x - 6 \geq 0

Multiply the terms

More Steps

x^{3} - 6 \geq 0

Rewrite the expression

x^{3} - 6 = 0

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

x^{3} = 0 + 6

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

x^{3} = 6

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

3 x^{3} = 36

Calculate

x = 36

Determine the test intervals using the critical values

x < 36 x > 36

Choose a value form each interval

x_{1} = 1 x_{2} = 3

To determine if x < 36 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < 36 is not a solution x_{2} = 3

To determine if x > 36 is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < 36 is not a solution x > 36 is the solution

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

x \geq 36 is the solution

Solution

x \geq 36

Alternative Form

x \in [36, + \infty)

Solve the inequality