SOLUTION: Why doesn't 256 r^2 + 289 = 0 have a real solution? And why can't it be solved using factorization?

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Question 807881: Why doesn't 256 r^2 + 289 = 0 have a real solution? And why can't it be solved using factorization?

Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+256r%5E2+%2B+289+=+0+
Subtract +289+ from both sides
+256r%5E2+=+-289+
Divide both sides by +256+
+r%5E2+=+-289%2F256+
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+r+ cannot be a real number because
there is no real number which, if you
square it, you get a negative number.
(+) x (+) = (+)
and, also
(-) x (-) = (+)
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Have you had lessons on imaginary numbers yet?
That's what you need to solve this

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Why doesn't 256 r^2 + 289 = 0 have a real solution? And why can't it be solved using factorization?
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256*r^2 + 289 = 0
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256*r^2 = -289
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Since the right side is negative, r^2 must be negative.
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But there is no Real Number whose square is negative.
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Note: The equation is solvable using complex numbers.
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Cheers,
Stan H.