For this case we have the following polynomial:
[tex]2x ^ 2 - 4x - 5 = 0
[/tex]
Rewriting we have:
[tex]2x ^ 2 - 4x = 5
x ^ 2 - 2x = 5/2[/tex]
Then, completing squares we have:
[tex]x ^ 2 - 2x + (-2/2) ^ 2 = 5/2 + (-2/2) ^ 2
[/tex]
Rewriting:
[tex]x ^ 2 - 2x + (-1) ^ 2 = 5/2 + (-1) ^ 2
x ^ 2 - 2x + 1 = 5/2 + 1
(x-1) ^ 2 = 7/2[/tex]
[tex]x-1 = +/- \sqrt{7/2} x = 1 +/- \sqrt{7/2}[/tex]
Then, the solutions are:
[tex]x1 = 1 + \sqrt{7/2} x2 = 1 - \sqrt{7/2} [/tex]
Answer:
[tex]x1 = 1 + \sqrt{7/2}
x2 = 1 - \sqrt{7/2} [/tex]
