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

##### 1 Answer

Nov 13, 2017

#### 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#