SOLUTION: Can you please help me? I have tried working it out but it doesn't check out right. (x+7)^3/2=27

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Question 123339: Can you please help me? I have tried working it out but it doesn't check out right.
(x+7)^3/2=27
Found 3 solutions by Earlsdon, bucky, MathLover1:
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
%28x%2B7%29%5E%283%2F2%29+=+27 Raise both sides to the 2/3 power.
%28%28x%2B7%29%5E%283%2F2%29%29%5E%282%2F3%29+=+27%5E%282%2F3%29
x%2B7+=+9
x+=+2

Answer by bucky(2100) About Me  (Show Source):
You can put this solution on YOUR website!
The way you wrote your problem it could be interpreted in several ways. It could be:
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%28x%2B7%29%5E3%2F2=27
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But I suspect that you meant:
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%28x%2B7%29%5E%283%2F2%29=27
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So I am going to work the second version in which the exponent is 3%2F2. If I am not correct
you will probably need to post your problem again.
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Starting with:
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%28x%2B7%29%5E%283%2F2%29=27
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You can use the power rule of exponents to rewrite the problem as:
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%28%28x%2B7%29%5E%281%2F2%29%29%5E3+=+27
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Notice that on the right side the 27 is equivalent to 3%5E3. Substitute 3 cubed for 27
and the equation then becomes:
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%28%28x%2B7%29%5E%281%2F2%29%29%5E3+=+3%5E3
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Take the cube root of both sides and the equation reduces to:
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%28x%2B7%29%5E%281%2F2%29+=+3
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Square both sides and the equation is then:
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%28x+%2B+7%29+=+9
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Subtract 7 from both sides and you have:
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x+=+2
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Check ... return to the original problem:
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%28x%2B7%29%5E%283%2F2%29=27
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Substitute 2 for 7 and you have:
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%282%2B7%29%5E%283%2F2%29+=+27
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Combine the 2 + 7 to get 9 and the problem then is:
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%289%29%5E%283%2F2%29+=+27
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You can then take the square root of 9 and cube it or cube 9 and take the square root of that
with the same result. The square root of 9 is 3 and if you cube 3 you get 27, making the
equation become 27 = 27. Or you can cube 9 and get 729. Then take the square root of 729
and get 27 ... again making the equation 27 = 27. Or, since 3/2 = 1.5, you can use a calculator
and raise 9 to the 1.5 power and you again get 27 ... once more making the equation 27 = 27.
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In any case x = 2 is a valid solution to the problem.
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Hope this helps you to understand the problem and how to work it through to a solution.
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Answer by MathLover1(3376) About Me  (Show Source):