Question

Solve 2x2 − 4x − 5 = 0 by completing the square.

Answer 1

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