Question

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

Answer 1

2(x^2-2x+1-1)+5=0
2(x-1)^2+3=0
(x-1)^2=-3/2
x-1=+-√-3÷2

\[x=1+√
`(-3)/(2)`\]
and \[x=1-√-3/2\]

Answer 2

Rewrite the right side of the equation

`2x^2-4x-5 = 0` in the following way:


`2x^2-4x-5 = 2(x^2-2x)-5=2(x^2-2x+1-1)-5=2((x-1)^2-1)-5=2(x-1)^2-2-5=2(x-2)^2-7`.
Then the equation is
`2(x-2)^2-7=0` and
`2(x-2)^2=7`.

So,
`(x-2)^2= (7)/(2)` and
`x-2=\pm \sqrt{ (7)/(2) }`
The equation has two solutions:
`x_1=2+ \sqrt{ (7)/(2) }` and
`x_2=2- \sqrt{ (7)/(2) }`.