Solve x^2 - 2x - 2 >0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \in (- \infty, - 3 + 1) \cup (3 + 1, + \infty)

Evaluate

x^{2} - 2 x - 2 > 0

Rewrite the expression

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

Add or subtract both sides

x^{2} - 2 x = 2

Add the same value to both sides

x^{2} - 2 x + 1 = 2 + 1

Simplify the expression

(x - 1)^{2} = 3

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

x - 1 = \pm 3

Separate the equation into 2 possible cases

x - 1 = 3 x - 1 = - 3

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

x = 3 + 1 x - 1 = - 3

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

x = 3 + 1 x = - 3 + 1

Determine the test intervals using the critical values

x < - 3 + 1 - 3 + 1 < x < 3 + 1 x > 3 + 1

Choose a value form each interval

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

To determine if x < - 3 + 1 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - 3 + 1 is the solution x_{2} = 1 x_{3} = 4

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

More Steps

x < - 3 + 1 is the solution - 3 + 1 < x < 3 + 1 is not a solution x_{3} = 4

To determine if x > 3 + 1 is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

More Steps

x < - 3 + 1 is the solution - 3 + 1 < x < 3 + 1 is not a solution x > 3 + 1 is the solution

Solution

x \in (- \infty, - 3 + 1) \cup (3 + 1, + \infty)

Show Solution