Concentration/Equilibrium Math Problem HELP PLEASE?

Concentration/Equilibrium Math Problem HELP PLEASE?Gout-a condition that results in joint swelling and pain-is caused by the formation of sodium urate NaC5H3N4 crystals within tendons, cartilage, and ligaments. Sodium urate will precipitate out of blood plasma when uric acid levels become abnormally high. This could happen as a result of eating too many rich foods and consuming too much alcohol, which is why gout is sometimes referred to as the "disease of kings."

If the sodium concentration in blood plasma is 0.140 M, and K_sp for sodium urate is 5.76*10^-8, what minimum concentration of urate would result in the precipitation of odium urate?

Dr.A
The equilibrium
C5H3N4O3Na <-------> C5H3N4O3- + Na+
requires that
Ksp = [C5H3N4O3-][Na+]
let x = mol/L sodium urate that dissolve : this will produce x mol/L urate and x mol/L Na+.
But there is arleady some Na+ so at equilibrium
[Na+]= 0.140 +x and [urate] = x

5.76 x 10^-8 = (0.140+x)(x)
since x has to be small compared to 0.140 we can assume 0.140+x = x.
this gives us the approximate equation
5.76 x 10^-8 = (0.140)(x)
x = [urate]=4.11 x 10^-7 M

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