Question

Find x:
0=(64/x^1/2)+(x/500)

Answer 1

try getting common denominators and combine the fractions.... then set the numerator equal to zero and solve.

Answer 2

how do I get common denominators when there's a square root in the denominator?

Answer 3

\[0 = \frac{ 64 }{ \sqrt{x} } + \frac{ x }{ 500 }\]
\[0=x+64\times500 / \sqrt{x} = \frac{ 32000}{ \sqrt{x} }\]

Answer 4

Calculating with ratios (sorry dont know the english name) help in many cases. I'm not sure if this is right though.

Answer 5

what happened to the x on the numerator?

Answer 6

sorry it was a typo. x+32000/sqrt(x)

Answer 7

ohh okay, so to find just x would I multiply the reciprocal of sqrt(x) on both sides?

Answer 8

I missed something. sec correcting..

Answer 9

alright

Answer 10

x*sqrt(x)=x^(3/2), so when you move x to left and add it to result you move the multiplied version of it. So result is \[\frac{ x^{3/2}+32000 }{ {\sqrt{x}} }\]

Answer 11

\[0=\frac{64}{\sqrt{x}}+\frac{x}{500}\]
Multiply both sides by square root of x
\[0=64+\frac{x ^{\frac{3}{2}}}{500}\]
\[-(64\times 500)=x ^{\frac{3}{2}}\]
\[(64\times 500)=-x ^{\frac{3}{2}}\]
Taking logs of both sides:
\[\ln (64\times 500)=\frac{3}{2}\ln (-x)\]
\[\frac{2}{3}\ln (64\times 500)=\ln (-x)\]
\[6.91566=\ln (-x)\]
From which we get the interesting result
\[-x=e ^{6.91566}=1008\]
If you substitute 1008 for x in the original equation it is a solution provided the negative option for the square root of x is taken.

Answer 12

I typed in 1008 and it says its incorrect

Answer 13

0=(64/x^1/2)+(x/500)
\(\Large 0=\frac{64}{\sqrt{x}}+\frac{x}{500} \)
\(\Large 0=\frac{64}{\sqrt{x}}\frac{500}{500}+\frac{x}{500}\frac{\sqrt{x}}{\sqrt{x}} \)
\(\Large 0=\frac{64 \cdot 500 +x^{\frac{3}{2}}}{500x^{\frac{1}{2}}} \)

Answer 14

now just set the numerator equal to zero and solve.... i believe the others did that for you....