Solving for X: 0.012M/(d-x)^2=M/x^2

[thomasrules]

For some reason i can't solve for x:

0.012M/(d-x)^2=M/x^2

I have M value: (5.98)(10)^24

d is: (3.84)(10)^5

 

[Yapper]

show your work

 

[thomasrules]

i started with cross multiplying:

0.012Mx^2=M(d-x)^2

0.012Mx^2=M(d^2-2dx+x^2)

then i divided both sides by the left side and crossed out M.

From there I don't know what to do

 

[BobG]

After you divided both sides by M and then divided both sides by .012, you should have wound up with:

$$x^2=\frac{d^2-2dx+x^2}{.012}$$

Split the right side up into three fractions:

$$x^2=\frac{d^2}{.012}-\frac{2dx}{.012}+\frac{x^2}{.012}$$

Substitute in your value for d. That should leave you with something you can work with.

 

[HallsofIvy]

Actually, I wouldn't divide both sides by 0.012, just because I don't like fractions!

0.012x²= d²- 2dx+ x² is the same as (subtract 0.012x² from both sides)
0.988x²- 2dx+ d²= 0.

With d= 3.85 x 10⁵, d²= 1.48225 x 10¹¹ so your equation is
0.988x²- (7.7 x 10⁵)x+ 1.48225 x 10¹¹= 0.

You can solve that with the quadratic formula.

 

[misogynisticfeminist]

does d in this case stand for difference like in calculus or is it just any other variable?

 

[dextercioby]

By,the looks of it,it's a dimensionful number...

Daniel.

PS.Got it,it's the mean distance Earth-Moon and M is the Earth's mass... And it's in Km.

 

[stunner5000pt]

couldnt you first divde M on both sides and then find the square root??

as in

$$\frac{0.012M}{(d-x)^2} = \frac{M}{x^2}$$
which then gives

$$\frac{0.012}{(d-x)^2} = \frac{1}{x^2}$$

and then find the square rooton both sides

$$\frac{\sqrt{0.012}}{d-x} = \frac{1}{x}$$

then cross multiply and solve without need for a quadratic??

 

[dextercioby]

I'm sorry,but it doesn't work that way.You need to consider the modulus when extracting sqrt,which would complicate the problem...

Daniel.

 

[jackal]

see i think it's this,
0.012M/(d-x)^2=M/x^2

cross multiply,

x^2/(d-x)^2=M/0.012M

x/(d-x)={1/0.012}^1/2 (that is sq root)

x/(d-x)=9.13

dividing the numerator & denominator by x

1/{(d/x) - 1}=9.13

{(d/x) - 1}=1/9.13
=0.11

(d/x)=1+.11
=1.11

since,d is: (3.84)(10)^5,we have

x=d/1.11
=(3.84)(10)^5/1.11
=345,945.95 units

 

[dextercioby]

see i think it's this,
0.012M/(d-x)^2=M/x^2

cross multiply,

x^2/(d-x)^2=M/0.012M

x/(d-x)={1/0.012}^1/2 (that is sq root)

THAT IS DEVIOUS...U should have a $$\pm$$ sign...


Daniel.

 

[jackal]

if its correct please tell me.

 

[dextercioby]

I thought i put in a very obvious way... It's wrong.By inappropriately extracting square root,u lost one (possibly viable) solution.

Daniel.