Question

How do you solve `2x^2 + 12x − 14 = 0` by completing the square?

Answer 1

`x=-7color(white)("XX")orcolor(white)("XX")x=+1`

Explanation:

`2x^2+12x-14=0`

`rarr2x^2+12x=14`

`rarr x^2+6x=7`

Now to "complete the square":
If `x^2+6x` are the first two terms of the expansion of a squared binomial: `(x+a)^2 = x^2+2ax+a^2`
then `2ax` must equal `6x`;
that is `a=3` and `a^2=9`

To "complete the square" we must add `color(magenta)(9)` to the expression,
but we can only legally do this if we add `color(magenta)9` to both sides of the equation:
`color(white)("XXX")x^2+6xcolor(magenta)(+9) = 7color(magenta)(+9)`

`color(white)("XXX")rarr (x+3)^2=16`

`color(white)("XXX")rarr x+3=+-4`

`color(white)("XXX")rarr x=-3+-4`

`color(white)("XXX")`which can be written as: `x=-7color(white)("X")orcolor(white)("X")x=1`