How do you solve the quadratic equation by completing the square: #v^2+6v-59=0#?

1 Answer
Jul 23, 2015

Answer:

#^v^2+6v-59 =0#
#color(white)("XXXX")##rarr##color(white)("XXXX")##v=-3+-2sqrt(17)#
#color(white)("XXXX")#(by completing the square)

Explanation:

#v^2+6v-59 = 0#
#color(white)("XXXX")#Move the constant to the right side (out of the way)
#v^2+6v = 59#
#color(white)("XXXX")#Add as the third term the value needed to make the right side a square
#v^2+6v+3^2 = 59+9#
#color(white)("XXXX")#Re-write right side as a squared binomial
#(v+3)^2 = 68#
#color(white)("XXXX")#Take the square root of both sides
#v+3 = +-sqrt(68) = +-2sqrt(17)#
#color(white)("XXXX")#Isolate #v# by subtracting #3# from both sides
#v = -3+-2sqrt(17)#