Question

How do you solve `v^2-17v+200=13v-43` by completing the square?

Answer 1

`v=15+-3sqrt2i`

Explanation:

`"rearrange into standard form "ax^2+bx+c=0`

`rArrv^2-30v+243=0`

`• " coefficient of "v^2" term must be 1, which it is"`

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

`rArrv^2+2(-15)vcolor(red)(+225)+243=0color(red)(+225)`

`rArr(v-15)^2=225-243=-18`

`"there are no real solutions"`

`color(blue)"take the square root of both sides"`

`rArrv-15=+-sqrt(-18)larr" note plus or minus"`

`rArrv-15=+-3sqrt2i`

`rArrv=15+-3sqrt2i`