What is 8v squared - 112v plus 320?

Answer 1

short answer

v = 10, 4

long answer (two methods)

method 1

factoring

8v2 - 112v + 320 = 0

factor out 8

8(v2 - 14v + 40) = 0

find two number that add to give -14 and multiply to give 40

in this case -10 and -4

8(v2 - 10v - 4v + 40) = 0

factor out v from the first two terms and -4 from the last two

8(v(v - 10) + 4(v - 10)) = 0

factor out (v-10)

8(v - 10)(v - 4) = 0

v = 10, 4

method 2

using the quadratic formula

8v2 - 112v + 320 = 0

in the form of ax2 + bx + c,

x = (-b +/- √(b2 - 4ac))/(2a)

plug in values for a, b and c

v = (-(-112) +/- √((-1122)-4(8)(320))/(2(8))

simplify in steps

v = (112 +/- √(12544 - 10240))/16

v = (112 +/- √2304)/16

v = (112 +/- 48)16

factor out 16 from the top

v = (16(7 +/- 3))/16

the 16's cancel

v = 7 +/- 3

v = 10, 4