Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
x∈(−∞,2−10+3)∪(210+3,+∞)
Evaluate
4x2−12x−1>0
Rewrite the expression
4x2−12x−1=0
Add or subtract both sides
4x2−12x=1
Divide both sides
44x2−12x=41
Evaluate
x2−3x=41
Add the same value to both sides
x2−3x+49=41+49
Simplify the expression
(x−23)2=25
Take the root of both sides of the equation and remember to use both positive and negative roots
x−23=±25
Simplify the expression
x−23=±210
Separate the equation into 2 possible cases
x−23=210x−23=−210
Solve the equation
More Steps

Evaluate
x−23=210
Move the constant to the right-hand side and change its sign
x=210+23
Write all numerators above the common denominator
x=210+3
x=210+3x−23=−210
Solve the equation
More Steps

Evaluate
x−23=−210
Move the constant to the right-hand side and change its sign
x=−210+23
Write all numerators above the common denominator
x=2−10+3
x=210+3x=2−10+3
Determine the test intervals using the critical values
x<2−10+32−10+3<x<210+3x>210+3
Choose a value form each interval
x1=−1x2=2x3=4
To determine if x<2−10+3 is the solution to the inequality,test if the chosen value x=−1 satisfies the initial inequality
More Steps

Evaluate
4(−1)2−12(−1)−1>0
Simplify
More Steps

Evaluate
4(−1)2−12(−1)−1
Evaluate the power
4×1−12(−1)−1
Any expression multiplied by 1 remains the same
4−12(−1)−1
Simplify
4+12−1
Calculate the sum or difference
15
15>0
Check the inequality
true
x<2−10+3 is the solutionx2=2x3=4
To determine if 2−10+3<x<210+3 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps

Evaluate
4×22−12×2−1>0
Simplify
More Steps

Evaluate
4×22−12×2−1
Multiply the terms
24−12×2−1
Multiply the numbers
24−24−1
Evaluate the power
16−24−1
Subtract the numbers
−9
−9>0
Check the inequality
false
x<2−10+3 is the solution2−10+3<x<210+3 is not a solutionx3=4
To determine if x>210+3 is the solution to the inequality,test if the chosen value x=4 satisfies the initial inequality
More Steps

Evaluate
4×42−12×4−1>0
Simplify
More Steps

Evaluate
4×42−12×4−1
Calculate the product
43−12×4−1
Multiply the numbers
43−48−1
Evaluate the power
64−48−1
Subtract the numbers
15
15>0
Check the inequality
true
x<2−10+3 is the solution2−10+3<x<210+3 is not a solutionx>210+3 is the solution
Solution
x∈(−∞,2−10+3)∪(210+3,+∞)
Show Solution
