Answer:
x < 1 -(√14)/2 or
1 +(√14)/2 < x
Explanation:
You want an algebraic solution to the inequality 2x²-4x-5 > 0.
Completing the square
We can factor out the leading coefficient from the variable terms and subtract the constant term to get ...
2(x² -2x) > 5
Dividing by 2 and adding 1 to complete the square, we have ...
x² -2x +1 > 5/2 +1
(x -1)² > 7/2
Solutions
Taking the square root gives us the pair of inequalities ...
-(√14)/2 > x -1 or
x -1 > (√14)/2
Adding 1 completes the solution
x < 1 -(√14)/2 or
1 +(√14)/2 < x
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Additional comment
A quadratic inequality of the form z² > c is not so different from an absolute value inequality of the form |z| > c. Each resolves to two inequalities with disjoint solution sets.