Solve x^2>=5 - ScanMath

Evaluate

x^{2} \geq 5

Move the expression to the left side

x^{2} - 5 \geq 0

Rewrite the expression

x^{2} - 5 = 0

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

x^{2} = 0 + 5

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

x^{2} = 5

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

x = \pm 5

Separate the equation into 2 possible cases

x = 5 x = - 5

Determine the test intervals using the critical values

x < - 5 - 5 < x < 5 x > 5

Choose a value form each interval

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

To determine if x < - 5 is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - 5 is the solution x_{2} = 0 x_{3} = 3

To determine if - 5 < x < 5 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 5 is the solution - 5 < x < 5 is not a solution x_{3} = 3

To determine if x > 5 is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < - 5 is the solution - 5 < x < 5 is not a solution x > 5 is the solution

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

x \leq - 5 is the solution x \geq 5 is the solution

Solution

x \in (- \infty, - 5] \cup [5, + \infty)

Solve the inequality