1. The problem statement, all variables and given/known data The mass of the Moon is 7.35*10^22kg. At some point between the Earth and the Moon, the force of gravitational attraction cancels out. Calculate where this will occur, relative to Earth. Me = 5.98*10^24 kg Mm = 7.35*10^22 kg D = 3.84*10^8 m g = 6.67*10^-11 Nm^2/kg^2 **Mx(object) = 1 kg 2. Relevant equations r(moon) + r(earth) = D r(earth) = D-r(moon) FeG = FmG G(MeMx)/r^2 = G(MmMx)/(D-r)^2 *I had some trouble deciding where to put the (D-r) 3. The attempt at a solution Here's where I had difficulty...I simplified the equation into a quadratic that yields two answers: r^2(Me-Mm) - 2DMe*r +MeD^2 = 0 Plugging in the numbers, I get: r = 4.319*10^8 m or r = 3.46*10^8 m (this appears to be the correct answer). I researched this question and found the equation: r = (D[Me-(MeMm)^1/2]) / (Me-Mm) I was wondering how to isolate r and simplify the equation in order to get it to look like the one above. I am having trouble understanding where the 'Mm' term in the '(MeMm)^1/2' came from; also, does the '^1/2' come from taking the square root or does it have something to do with the '2' in the initial equation being taken out? Aside, what is a suitable explanation regarding the existence of the fallacious answer in the initial unsimplified quadratic? Thank you very much, I really appreciate the help.