Question

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

Answer 1

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`