Solve 25-x^2 > 0 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

- 5 < x < 5

Alternative Form

x \in (- 5, 5)

Evaluate

25 - x^{2} > 0

Rewrite the expression

25 - x^{2} = 0

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

- x^{2} = 0 - 25

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

- x^{2} = - 25

Change the signs on both sides of the equation

x^{2} = 25

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

x = \pm 25

Simplify the expression

More Steps

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} = - 6 x_{2} = 0 x_{3} = 6

To determine if x < - 5 is the solution to the inequality,test if the chosen value x = - 6 satisfies the initial inequality

More Steps

x < - 5 is not a solution x_{2} = 0 x_{3} = 6

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 not a solution - 5 < x < 5 is the solution x_{3} = 6

To determine if x > 5 is the solution to the inequality,test if the chosen value x = 6 satisfies the initial inequality

More Steps

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

Solution

- 5 < x < 5

Alternative Form

x \in (- 5, 5)

Show Solution