Solve for x

[matlabnoob]

Hi - having a bit of a slow moment with my algebra. Can I get some help solving for x in the following expression? Thank you!
Note: the 1s and 2s following each separate term are subscripts, and the entire equation is equal to 0

 

[Deleted member 4993]

Hi - having a bit of a slow moment with my algebra. Can I get some help solving for x in the following expression? Thank you!
Note: the 1s and 2s following each separate term are subscripts, and the entire equation is equal to 0


View attachment 23618

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[matlabnoob]

Hi! I actually got the answer! Please feel free to remove the post. Thank you.

 

[topsquark]

Hi! I actually got the answer! Please feel free to remove the post. Thank you.

Why don't you share your solution? Someone else might benefit from it.

-Dan

 

[JeffM]

In response to topsquark


[MATH]\dfrac{1}{\sigma_1^2} * \{2a_1(y_1 + a_1x)\} + \dfrac{1}{\sigma_2^2} * \{2a_2 * (y_2 + a_2x)\} = 0 \implies [/MATH]
[MATH]2a_1(y_1 + a_1x) + \dfrac{\sigma_1^2}{\sigma_2^2} * \{ 2a_2(y_2 + a_2x)\} = \sigma_1^2 * 0 = 0 \implies[/MATH]
[MATH]2a_1\sigma_2^2(y_1 + a_1x) + 2a_2\sigma_1^2(y_2 + a_2x) = \sigma_2^2 * 0 = p \implies[/MATH]
[MATH]x(2a_1^2 \sigma_2^2 + 2a_2^2 \sigma_1^2) + 2a_1 \sigma_2^2 y_1 + 2a_2 \sigma_1^2 y_2 = 0 \implies[/MATH]
[MATH]x = - \ \dfrac{2a_1 \sigma_2^2 y_1 + 2a_2 \sigma_1^2 y_2}{2a_1^2 \sigma_2^2 + 2a_2^2 \sigma_1^2}.[/MATH]