SOLUTION: 6w+(23w^1/2)-104=0

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Question 949096: 6w+(23w^1/2)-104=0
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
6w%2B%2823w%5E1%2F2%29-104=0


What about this: 6w%2B%2823w%5E%281%2F2%29%29-104=0
?


That can be rewritten,
6w%2B%2823sqrt%28w%29%29-104=0

To begin solving,
23sqrt%28w%29=104-6w
%2823sqrt%28w%29%29%5E2=%28104-6w%29%5E2
23%2Aw=%28104-6w%29%5E2
highlight_green%286w%5E2%2B23w-104=0%29

Now easier to continue. Use general solution formula.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

6w+(23w^1/2)-104=0
highlight%286w+%2B+23w%5E%281%2F2%29+-+104+=+0%29

Let highlight%28a+=+w%5E%281%2F2%29%29  

Then highlight%286w+%2B+23w%5E%281%2F2%29+-+104+=+0%29 becomes: 6a%5E2+%2B+23a+-+104+=+0

6a%5E2+%2B+39a+-+16a+-+104+=+0

3a(2a + 13) – 8(2a + 13) = 0

(3a – 8)(2a + 13) = 0

3a – 8 = 0                   OR                  2a + 13 = 0

a+=+8%2F3                        OR                  a+=+-+13%2F2            



highlight%288%2F3+=+w%5E%281%2F2%29%29 ---------- Substituting 8%2F3 for a

highlight%28%288%2F3%29%5E2+=+w%5E%28%281%2F2%29+%2A+2%29%29 ---- Squaring both sides

highlight_green%2864%2F9+=+w%29



-+13%2F2+=+w%5E%281%2F2%29 ---------- Substituting -+13%2F2 for a

No expression raised to a power results in a negative expression (< 0), so w+=+169%2F4 is an EXTRANEOUS solution.

Therefore, only solution is: highlight_green%28w+=+64%2F9%29