# (#(x+6)/(x^(1/2))=35#) ( #(x+1)/(x)#=?)

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Given:

#(x+6)/x^(1/2) = 35#

Multiply both sides by

#x+6 = 35x^(1/2)#

Square both sides to get:

#x^2+12x+36 = 1225x#

Subtract

#x^2-1213x+36 = 0#

Next note that we want to find:

#(x+1)/x = 1+1/x#

Multiplying the quadratic we have found by

#36(1/x)^2-1213(1/x)+1 = 0#

So by the quadratic formula we find:

#1/x = (1213+-sqrt((-1213)^2-4(36)(1)))/(2(36))#

#color(white)(1/x) = (1213+-sqrt(1471369-144))/72#

#color(white)(1/x) = (1213+-sqrt(1471225))/72#

#color(white)(1/x) = (1213+-35sqrt(1201))/72#

So:

#(x+1)/x = 1+1/x = 1285/72+-35/72sqrt(1201)#

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1

#### Explanation:

Solve for x:

I chose to square both sides in order to get rid of the square root.

I don't think I can factor this, so I'm going to apply the quadratic formula instead!

Now all you have to do is plug

Describe your changes (optional) 200