Solve -x^2 2x 8 ≥ 0

Evaluate

- x^{2} \times 2 x \times 8 \geq 0

Multiply

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- 16 x^{3} \geq 0

Rewrite the expression

- 16 x^{3} = 0

Change the signs on both sides of the equation

16 x^{3} = 0

Rewrite the expression

x^{3} = 0

The only way a power can be 0 is when the base equals 0

x = 0

Determine the test intervals using the critical values

x < 0 x > 0

Choose a value form each interval

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

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

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x < 0 is the solution x_{2} = 1

To determine if x > 0 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

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x < 0 is the solution x > 0 is not a solution

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

x \leq 0 is the solution

Solution

x \leq 0

Alternative Form

x \in (- \infty, 0]

Solve the inequality