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# Algebra

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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:

$$c - 4 = \pm 2i$$

$$\color{brown}\boxed{ c = 4 \pm2i}$$