Solve x^2<20 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

- 25 < x < 25

Alternative Form

x \in (- 25, 25)

Evaluate

x^{2} < 20

Move the expression to the left side

x^{2} - 20 < 0

Rewrite the expression

x^{2} - 20 = 0

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

x^{2} = 0 + 20

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

x^{2} = 20

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

x = \pm 20

Simplify the expression

More Steps

x = \pm 25

Separate the equation into 2 possible cases

x = 25 x = - 25

Determine the test intervals using the critical values

x < - 25 - 25 < x < 25 x > 25

Choose a value form each interval

x_{1} = - 5 x_{2} = 0 x_{3} = 5

To determine if x < - 25 is the solution to the inequality,test if the chosen value x = - 5 satisfies the initial inequality

More Steps

x < - 25 is not a solution x_{2} = 0 x_{3} = 5

To determine if - 25 < x < 25 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 25 is not a solution - 25 < x < 25 is the solution x_{3} = 5

To determine if x > 25 is the solution to the inequality,test if the chosen value x = 5 satisfies the initial inequality

More Steps

x < - 25 is not a solution - 25 < x < 25 is the solution x > 25 is not a solution

Solution

- 25 < x < 25

Alternative Form

x \in (- 25, 25)

Show Solution