Solve x^2-619>=0 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \in (- \infty, - 619] \cup [619, + \infty)

Evaluate

x^{2} - 619 \geq 0

Rewrite the expression

x^{2} - 619 = 0

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

x^{2} = 0 + 619

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

x^{2} = 619

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

x = \pm 619

Separate the equation into 2 possible cases

x = 619 x = - 619

Determine the test intervals using the critical values

x < - 619 - 619 < x < 619 x > 619

Choose a value form each interval

x_{1} = - 26 x_{2} = 0 x_{3} = 26

To determine if x < - 619 is the solution to the inequality,test if the chosen value x = - 26 satisfies the initial inequality

More Steps

x < - 619 is the solution x_{2} = 0 x_{3} = 26

To determine if - 619 < x < 619 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 619 is the solution - 619 < x < 619 is not a solution x_{3} = 26

To determine if x > 619 is the solution to the inequality,test if the chosen value x = 26 satisfies the initial inequality

More Steps

x < - 619 is the solution - 619 < x < 619 is not a solution x > 619 is the solution

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

x \leq - 619 is the solution x \geq 619 is the solution

Solution

x \in (- \infty, - 619] \cup [619, + \infty)

Show Solution