How do I use the quadratic formula to solve 2+5r−1=12(r−1)2?

1 Answer
Amory W.
Aug 22, 2014

The answers are −3,52.

You may be tempted to expand r−1, but let's use substitution: y=r−1

r=y+1

We have an NPV: r=1

2+5y=12y2
2y2+5y=12
2y2+5y−12=0
y=−5±√52−4(2)(−12)2(2)
=−5±√25+964
=−5±√1214
=−5±114
y=−4,32

You may be excited to get an answer and stop, but remember that we used substitution, so substitute back: r=y+1

r=−3,52

This does not conflict with the NPV, so the answer is good.

If you expand, you would have got:

2r2+r−15=0

Then you would use the quadratic and the answer would be the same.

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