Find all values of c such that c/(c-5) = 4/(c-4). Help, Please?

1 Answer

There are no real values of c that will make this equation work. However, there are imaginary solutions: c=-4+2i, -4-2i

Explanation:

c/(c-5)=4/(c-4)

Cross multiply:

c(c-4)=4(c-5)

Distribute:

c^2-4c=4c-20

Set equal to 0:

c^2-8c+20=0

I'll use the quadratic formula:

x = (-b \pm sqrt(b^2-4ac)) / (2a)

with a=1, b=-8,c=20

x = (-8 \pm sqrt((-8)^2-4(1)(20))) / (2(1))

x = (-8 \pm sqrt(64-80)) / 2

There are no real solutions to this problem. There are, however, imaginary solutions:

x = (-8 \pm sqrt(-16)) / 2 =(-8pm4i)/2

x=-4+2i, -4-2i