Question

How do you solve `2x^2 – 2x – 3 = 0` by completing the square?

Answer 1

`x=1/2+sqrt7/2` and
`x=1/2-sqrt7/2`

Explanation:

In `2x^2-2x-3=0`, let us first divide this by `2` and we get `x^2-x-3/2=0`. As the coefficient of `x` is `-1`, let us add and subtract `(-1)^2/4` or `1/4`, which gives us

`x^2-x+1/4-3/2-1/4=0` or

`(x-1/2)^2-7/4=0` or

`(x-1/2)^2-(sqrt7/2)^2=0` or

`(x-1/2-sqrt7/2)(x-1/2+sqrt7/2)=0` or

`x=1/2+-sqrt7/2`