Solve x^2-2x-15<0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

- 3 < x < 5

Alternative Form

x \in (- 3, 5)

Evaluate

x^{2} - 2 x - 15 < 0

Rewrite the expression

x^{2} - 2 x - 15 = 0

Factor the expression

More Steps

(x - 5) (x + 3) = 0

When the product of factors equals 0,at least one factor is 0

x - 5 = 0 x + 3 = 0

Solve the equation for x

More Steps

x = 5 x + 3 = 0

Solve the equation for x

More Steps

x = 5 x = - 3

Determine the test intervals using the critical values

x < - 3 - 3 < x < 5 x > 5

Choose a value form each interval

x_{1} = - 4 x_{2} = 1 x_{3} = 6

To determine if x < - 3 is the solution to the inequality,test if the chosen value x = - 4 satisfies the initial inequality

More Steps

x < - 3 is not a solution x_{2} = 1 x_{3} = 6

To determine if - 3 < x < 5 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < - 3 is not a solution - 3 < 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 < - 3 is not a solution - 3 < x < 5 is the solution x > 5 is not a solution

Solution

- 3 < x < 5

Alternative Form

x \in (- 3, 5)

Show Solution