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.Find all values of c such that c/(c - 5) = 4/(c + 4).

 Apr 2, 2022
 #1
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Cross multiply: 

\(c^2 - 4c = 4c+20\)

Simplify into standard form: 

\(c^2-8c+20 = 0\)

Complete the square: 

\((c - 4)^2 + 4 = 0\)

Subtract 4 from both sides: 

\((c-4)^2 = -4\)

Take the square root of both sides: 

\(c - 4 = \pm 2i\)

Add 4 to both sides: 

\(\color{brown}\boxed{ c = 4 \pm2i}\)

 Apr 2, 2022

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