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 = +/- √(7/2) x = 1 +/- √(7/2)`
Then, the solutions are:

`x1 = 1 + √(7/2) x2 = 1 - √(7/2)`
Answer:

`x1 = 1 + √(7/2) x2 = 1 - √(7/2)`