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January 5th, 2014, 02:31 PM   #1
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How to solve these problems algebraically?

3x^2 + 192 = 0

x^3 + 125 = 0

I don't know where to begin for the first problem. I assumed it would be factoring a sum of squares but 192 is not a square. For the second one I am guessing it is a sum of cubes problem?

Second one I got (x + 5)(x^2 - 5x + 25). Would I need to find the zeros and how would I do that? Not sure what it means to "solve" algebraically.
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January 5th, 2014, 02:46 PM   #2
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Re: How to solve these problems algebraically?

1. You can't factor a sum of squares with real numbers. Otherwise, 3x + 192 = 3(x + 64) = 3(x - 8i)(x + 8i), hence the roots are 8i and -8i.

2. x + 125 = (x + 5)(x - 5x + 25) = 0 implies x = -5 is a solution. Can you find x if x - 5x + 25 = 0?
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January 5th, 2014, 03:50 PM   #3
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Re: How to solve these problems algebraically?

Hello, GrannySmith!

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