Alan

$$\sqrt{x-5}+5=0$$

Subtract 5 from both sides

$$\sqrt{x-5}=-5$$

Square both sides

$$x-5=(-5)^2$$

or

$$x-5=25$$

Add 5 to both sides

$$x=30$$

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The LCM of 8847 and 2532 is 7466868

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There is no closed form analytical solution to a general 6th order polynomial.  You would usually need to use a numerical technique.  

There are some specific 6th order polynomials that do allow of an analytical solution (e.g. (x-n)⁶=0), but generally you have to use a numerical approach.  Do you have a specific polynomial in mind

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Nice picture Melody.  This should really help people understand the problem and the solution.  An example of a picture being worth a thousand words!

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Thanks Chris.  I was a little lazy here and just got Mathcad to solve the equations for me!

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This can be written as: (cos(t) + 2)(2cos(t) - 1) = 0

1. cos(t) = -2  is not possible, so we must have

2. cos(t) = 1/2, which means that t = ±60°

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The relative speed is 2 km/minute.  That is, assume one of the trains is stationary and the other is travelling at the combined speed of both.

The total distance to be travelled before they completely pass each other is (1/2 + 2/3)km = 7/6 km.

Total time is therefore (7/6)/2 minutes = 7/12 minutes = 7*60/12 seconds = 7*5 seconds = 35 seconds

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Molecular weight of water is 18, so there are 150/18 moles of H₂O.  As there is one atom of Oxygen for each molecule of water there are 150/18 moles of Oxygen.

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(4p - 5)(2p² + 3)