Question

Complete the square: `color(white)("d")m^2+20m=-5` How would you work this one out? (I don’t know how to do it if the c value is missing)

Answer 1

`(m+10)^2-95=0`

Explanation:

`"to "color(blue)"complete the square"`

`• " ensure the coefficient of the squared term is 1"`

`m^2+20m=-5larr"coefficient of "m^2" is 1"`

`• " add "(1/2"coefficient of m term")^2" to both sides"`

`m^2+2(10)mcolor(red)(+100)=-5color(red)(+100)`

`=(m+10)^2=95`

`"or "(m+10)^2-95=0`

Answer 2

See explanation
Observe that in the graph both

#color(red)(m^2+20m+5=0) and color(blue)((m+10)^2-95=0)#

Are the same thing. They completely overlap.

Explanation:

For a very in-depth explanation of the method have a look at my solution: https://socratic.org/s/aKFa5Suf

In this case the c is there but it is 'hidden'. In that it looks like the value for `y`

Add `5` to both sides giving

`m^2+20m+5=0`

Set as `m^2+20m+5=0=y`

Solve for `y=0`

Write as `(m^2+20m)+k+5=0`

Take the power outside the brackets

`(m+20m)^2+k+5=0`

Remove the m from `20m`

`(m+20)^2+k+5=0`

Halve the 20

`(m+10)^2+k+5=0`

In making these changes we have introduced a value that is not in the original equation. So we need to remove it (subtraction). This is where `k` comes in.

Set `10^2+k=0 => k=-100`

`(m+10)^2-100+5=0`

`(m+10)^2-95=0 larr" The question only askes for this stage"`