Question

How do you solve `m^2 + 2m + 6` by completing the square?

Answer 1

Also look at http://socratic.org/s/asBgAcAP

`(m+1)^2+5`

Explanation:

Given: `" "m^2+2m+6`

Using short cuts - By sight we have:

`(m+1)^2+5`

'~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 1")`

Add brackets`->(m^2+2m)+6`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 2")`

Take the power outside the bracket`->(m+2m)^2+6`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 3")`

Remove the `m" from "2m ->(m+2)^2+6`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 4")`

Multiply the constant inside the brackets
by `1/2" "->(m+[1/2xx2])^2+6`

`= (m+1)^2+6`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 5")`

When squaring the brackets you get `m^2+2m+color(red)(1^2)+6`

The `color(red)(1^2)` is not in the original equation so it is an error. It has to be removed by including `color(magenta)(-1)`

`(m+1)^2color(magenta)(-1)+6`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Step 6")`

Answer is:`" "color(green)((m+1)^2+5)`