Solve x^2 -4x -3 < 0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

- 7 + 2 < x < 7 + 2

Alternative Form

x \in (- 7 + 2, 7 + 2)

Evaluate

x^{2} - 4 x - 3 < 0

Rewrite the expression

x^{2} - 4 x - 3 = 0

Add or subtract both sides

x^{2} - 4 x = 3

Add the same value to both sides

x^{2} - 4 x + 4 = 3 + 4

Simplify the expression

(x - 2)^{2} = 7

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

x - 2 = \pm 7

Separate the equation into 2 possible cases

x - 2 = 7 x - 2 = - 7

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

x = 7 + 2 x - 2 = - 7

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

x = 7 + 2 x = - 7 + 2

Determine the test intervals using the critical values

x < - 7 + 2 - 7 + 2 < x < 7 + 2 x > 7 + 2

Choose a value form each interval

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

To determine if x < - 7 + 2 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - 7 + 2 is not a solution x_{2} = 2 x_{3} = 6

To determine if - 7 + 2 < x < 7 + 2 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - 7 + 2 is not a solution - 7 + 2 < x < 7 + 2 is the solution x_{3} = 6

To determine if x > 7 + 2 is the solution to the inequality,test if the chosen value x = 6 satisfies the initial inequality

More Steps

x < - 7 + 2 is not a solution - 7 + 2 < x < 7 + 2 is the solution x > 7 + 2 is not a solution

Solution

- 7 + 2 < x < 7 + 2

Alternative Form

x \in (- 7 + 2, 7 + 2)

Show Solution