Solve n^2-6n-10<0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for n

- 19 + 3 < n < 19 + 3

Alternative Form

n \in (- 19 + 3, 19 + 3)

Evaluate

n^{2} - 6 n - 10 < 0

Rewrite the expression

n^{2} - 6 n - 10 = 0

Add or subtract both sides

n^{2} - 6 n = 10

Add the same value to both sides

n^{2} - 6 n + 9 = 10 + 9

Simplify the expression

(n - 3)^{2} = 19

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

n - 3 = \pm 19

Separate the equation into 2 possible cases

n - 3 = 19 n - 3 = - 19

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

n = 19 + 3 n - 3 = - 19

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

n = 19 + 3 n = - 19 + 3

Determine the test intervals using the critical values

n < - 19 + 3 - 19 + 3 < n < 19 + 3 n > 19 + 3

Choose a value form each interval

n_{1} = - 2 n_{2} = 3 n_{3} = 8

To determine if n < - 19 + 3 is the solution to the inequality,test if the chosen value n = - 2 satisfies the initial inequality

More Steps

n < - 19 + 3 is not a solution n_{2} = 3 n_{3} = 8

To determine if - 19 + 3 < n < 19 + 3 is the solution to the inequality,test if the chosen value n = 3 satisfies the initial inequality

More Steps

n < - 19 + 3 is not a solution - 19 + 3 < n < 19 + 3 is the solution n_{3} = 8

To determine if n > 19 + 3 is the solution to the inequality,test if the chosen value n = 8 satisfies the initial inequality

More Steps

n < - 19 + 3 is not a solution - 19 + 3 < n < 19 + 3 is the solution n > 19 + 3 is not a solution

Solution

- 19 + 3 < n < 19 + 3

Alternative Form

n \in (- 19 + 3, 19 + 3)

Show Solution