algebra word problem help needed?

Question

venture capital- Henry inversted $12,000 in a new restaurant. When the restaurant was sold two years later, he received $27,000. find his average annual return by solving the equation 12,000(1+r)^2= 27,000

Answer 1

12,000(1+r)^2= 27,000

(1+r)^2 = 27000/12000 = 27/12 = 9/4
(1+r)^2 = r^2 +2r +1 =9/4= 2.25
r^2 +2r +1-2.25 = r^2 +2r -1.25 =0
discriminant = 4 +4(1.25) =9
Solutions are:
r1= (-2-3)/2 = -5/2 =-2.5
r2= (-2+3)/2 =0.5
verification:
for r1= -2.5
substitute solution r =2.5 into the equation
12,000(1+r)^2= 27,000, we get
12000(1-2.5)^2 = 12000((-1.5)^2 =27,000
r1 =-2.5 is a a possible solution (but is negative, suggests a loss)
same for r2 = 0.5

but he made money, therefore only positive returns are allowed
the solution is
r =0.5

Answer 2

12,000(1+r)^2= 27,000

First you move 12,000 over by dividing
(1+r)^2 = 27,000/12,000 = 2.25

Then take the square root of both sides
1+r = 1.5

and subtract 1.
r = .5

Answer 3

12,000(1+r)^2 = 27,000
12,000(1 + 2r + r^2 = 27,000
12,000 + 24,000r + 12,000r^2 =27,000
12,000r^2 + 24,000r - 15,000 = 0 simplify by diving 3000
3000(4r^2 + 8r - 5 ) = 0
3000(2r-1)(2r+5) = 0
r= 1/2r x 3000 = 1500 or r= -5/2r x 3000 = -7500
So the result is 1500 because it is unlikely for the average return to be a negative number

Answer 4

12000*(1+r)^2=27000
(1+r)^2=27000/12000 divide both sides by 12000
(1+r)^2=2.25 simplify
1+r=sqrtroot(2.25) take the square root of both sides
1+r=2.25^.5 same thing in computer notation
1+r=1.5 sqrt of 2.25 is 1.5
r=1.5-1 subtract 1 from each side
r=.5 and simplify


proof

12000*(1+.5)^2=
12000*(1.5)^2=
12000*2.25=
27000= 27000 every thing balances
so r=.5 (r=1/2 in case you can't see the decimal point)

hope this helps

Answer 5

1+r = SQRT (27/12 ) = SQRT (2.25) = 1.5.

r = 50%.