How do you solve #3v ^ { 2} + 8v - 35= 0#?

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Answer 1 · 2018-01-26T20:25:04

#v = 7/3# or #v = -5#

to factorise:

multiply coefficients of first and last term together:
#3 * -35 = 105#

firstly, #8v# can be changed into #2# numbers that both add to #8# and multiply to #-105#.

#15 - 7 = 8#
#15v - 7v = 8v#

#15 * -7 = -105#

#3v^2 + 8v - 35 = 3v^2 + 15v - 7v - 35#

then factorise:

#3v^2 + 15v = 3v (v + 5)#

#-7v - 35 = -7(v+5)#

add grouped terms together:

#3v (v+5) -7 (v+5) = (3v - 7) (v+5)#

to solve:

#(3v - 7)(v + 5) = 0#

#3v - 7 = 0 -> 3v = 7#

#v = 7/3#

#v + 5 = 0 -> v = -5#

#v = 7/3# or #-5#