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**1. Homework Statement**

Objects with masses of 200kg and 500kg are separated by 0.4m a)Find the net gravitational force exerted by these objects on a 50kg object placed midway between them. b) At what position (other than infinitely remote ones) can the 50 kg object be placed so as to experience a net force of zero?

I have solved a), everything below is for part b)

I'm solving for a problem right now and I'm having difficulties in factoring. =P

Trying out Latex, it may take a while.

**2. Homework Equations**

[tex]0=\frac{Gm_{1}m_{3}}{-r_{1}{}^2} + \frac{Gm_{2}m_{3}}{r_{2}{}^2}[/tex]

**3. The Attempt at a Solution**

[tex]0=\frac{Gm_{1}m_{3}}{-r_{1}{}^2} + \frac{Gm_{2}m_{3}}{r_{2}{}^2}[/tex]

[tex]0=Gm_{3}(\frac{m_1}{-r_{1}{}^2} + \frac{m_2}{r_{2}{}^2})[/tex]

[tex]0=\frac{m_1}{-r_{1}{}^2} + \frac{m_2}{r_{2}{}^2}[/tex]

[tex]0=m_{1}r_{2}{}^2 - m_{2}r_{1}{}^2[/tex]

[tex]0=(200{}kg)r_{2}{}^2 - (500{}kg)r_{1}{}^2[/tex]

*Since there are two unknown variables, you need a second equation:*[tex]0.4m=r_{1} + r_{2}[/tex]

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I just don't know how to factor:

[tex]0=(200{}kg)r_{2}{}^2 - (500{}kg)r_{1}{}^2[/tex] to make it in [tex](r_{1}+r_{2})(r_{1} - r_{2})[/tex] form. Can someone show me the simple factoring that I've forgotten? xP

I just don't know how to factor:

[tex]0=(200{}kg)r_{2}{}^2 - (500{}kg)r_{1}{}^2[/tex] to make it in [tex](r_{1}+r_{2})(r_{1} - r_{2})[/tex] form. Can someone show me the simple factoring that I've forgotten? xP

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