Question #270b3

2 Answers
Dec 14, 2017

v=-6" or "v=1v=6 or v=1

Explanation:

"rearrange and equate to zero"rearrange and equate to zero

rArr7v^2+35v-42=0larrcolor(blue)"standard form"7v2+35v42=0standard form

"take out a "color(blue)"common factor of 7"take out a common factor of 7

rArr7(v^2+5v-6)=07(v2+5v6)=0

"the factors of - 6 which sum to + 5 are + 6 and - 1"the factors of - 6 which sum to + 5 are + 6 and - 1

rArr7(v+6)(v-1)=07(v+6)(v1)=0

"equate each factor to zero and solve for v"equate each factor to zero and solve for v

v+6=0rArrv=-6v+6=0v=6

v-1=0rArrv=1v1=0v=1

"the solutions are "v=-6" or "v=1the solutions are v=6 or v=1

Dec 14, 2017

v=1 or -6v=1or6

Explanation:

7v^2 -42 = -35v7v242=35v

7v^2+35v -42 = 07v2+35v42=0

7(v^2+5-6)=07(v2+56)=0

v^2+5-6=0v2+56=0

(v+6)(v-1)=0(v+6)(v1)=0

Using the 0 product property (if ab=0ab=0, then a =0 or b= 0a=0orb=0)

v+6=0v+6=0
=>v=-6v=6

v-1=0v1=0
v=1v=1