Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
x=−1
Evaluate
−x2−2x−1<0
Rewrite the expression
−x2−2x−1=0
Use a2+2ab+b2=(a+b)2 to factor the expression
−(x+1)2=0
Divide the terms
(x+1)2=0
Simplify the expression
x+1=0
Move the constant to the right-hand side and change its sign
x=0−1
Removing 0 doesn't change the value,so remove it from the expression
x=−1
Determine the test intervals using the critical values
x<−1x>−1
Choose a value form each interval
x1=−2x2=0
To determine if x<−1 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps
Evaluate
−(−2)2−2(−2)−1<0
Simplify
More Steps
Evaluate
−(−2)2−2(−2)−1
Multiply the numbers
−(−2)2+4−1
Apply the inverse property of addition
−1
−1<0
Check the inequality
true
x<−1 is the solutionx2=0
To determine if x>−1 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps
Evaluate
−02−2×0−1<0
Any expression multiplied by 0 equals 0
−02−0−1<0
Simplify
More Steps
Evaluate
−02−0−1
Calculate
−0−0−1
Removing 0 doesn't change the value,so remove it from the expression
−1
−1<0
Check the inequality
true
x<−1 is the solutionx>−1 is the solution
Solution
x=−1
Show Solution