Solve m^2-6m-3<0 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for m

- 23 + 3 < m < 23 + 3

Alternative Form

m \in (- 23 + 3, 23 + 3)

Evaluate

m^{2} - 6 m - 3 < 0

Rewrite the expression

m^{2} - 6 m - 3 = 0

Add or subtract both sides

m^{2} - 6 m = 3

Add the same value to both sides

m^{2} - 6 m + 9 = 3 + 9

Simplify the expression

(m - 3)^{2} = 12

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

m - 3 = \pm 12

Simplify the expression

m - 3 = \pm 23

Separate the equation into 2 possible cases

m - 3 = 23 m - 3 = - 23

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

m = 23 + 3 m - 3 = - 23

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

m = 23 + 3 m = - 23 + 3

Determine the test intervals using the critical values

m < - 23 + 3 - 23 + 3 < m < 23 + 3 m > 23 + 3

Choose a value form each interval

m_{1} = - 1 m_{2} = 3 m_{3} = 7

To determine if m < - 23 + 3 is the solution to the inequality,test if the chosen value m = - 1 satisfies the initial inequality

More Steps

m < - 23 + 3 is not a solution m_{2} = 3 m_{3} = 7

To determine if - 23 + 3 < m < 23 + 3 is the solution to the inequality,test if the chosen value m = 3 satisfies the initial inequality

More Steps

m < - 23 + 3 is not a solution - 23 + 3 < m < 23 + 3 is the solution m_{3} = 7

To determine if m > 23 + 3 is the solution to the inequality,test if the chosen value m = 7 satisfies the initial inequality

More Steps

m < - 23 + 3 is not a solution - 23 + 3 < m < 23 + 3 is the solution m > 23 + 3 is not a solution

Solution

- 23 + 3 < m < 23 + 3

Alternative Form

m \in (- 23 + 3, 23 + 3)

Show Solution