Solve x^4 - 29x^2 100 >= 0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \in (- \infty, - 1029] \cup [1029, + \infty) \cup {0}

Evaluate

x^{4} - 29 x^{2} \times 100 \geq 0

Multiply the terms

x^{4} - 2900 x^{2} \geq 0

Rewrite the expression

x^{4} - 2900 x^{2} = 0

Factor the expression

x^{2} (x^{2} - 2900) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{2} - 2900 = 0

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

x = 0 x^{2} - 2900 = 0

Solve the equation

More Steps

x = 0 x = 1029 x = - 1029

Determine the test intervals using the critical values

x < - 1029 - 1029 < x < 0 0 < x < 1029 x > 1029

Choose a value form each interval

x_{1} = - 55 x_{2} = - 27 x_{3} = 27 x_{4} = 55

To determine if x < - 1029 is the solution to the inequality,test if the chosen value x = - 55 satisfies the initial inequality

More Steps

x < - 1029 is the solution x_{2} = - 27 x_{3} = 27 x_{4} = 55

To determine if - 1029 < x < 0 is the solution to the inequality,test if the chosen value x = - 27 satisfies the initial inequality

More Steps

x < - 1029 is the solution - 1029 < x < 0 is not a solution x_{3} = 27 x_{4} = 55

To determine if 0 < x < 1029 is the solution to the inequality,test if the chosen value x = 27 satisfies the initial inequality

More Steps

x < - 1029 is the solution - 1029 < x < 0 is not a solution 0 < x < 1029 is not a solution x_{4} = 55

To determine if x > 1029 is the solution to the inequality,test if the chosen value x = 55 satisfies the initial inequality

More Steps

x < - 1029 is the solution - 1029 < x < 0 is not a solution 0 < x < 1029 is not a solution x > 1029 is the solution

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

x \leq - 1029 is the solution x \geq 1029 is the solution x = 0

Solution

x \in (- \infty, - 1029] \cup [1029, + \infty) \cup {0}

Show Solution