Question

G=x-c/x. for x

how do yoy make this an equation for x? help

Answer 1

1.

`\displaystyle \text{if }\quad G=x- (C)/(x) \\\\`


`x \\eq 0`

Multiply both sides by x:


`\displaystyle Gx=x\bigg(x- (C)/(x)\bigg )\\\\Gx=x^2-C`

Subtract from both sides Gx:

`Gx-Gx=x^2-C-Gx\\x^2-Gx-C=0`

Then solve this equation:


`\displaystyle x^2-Gx-C=0\\\\x_(1,2)= (G\pm √(G^2+4C) )/(2)`

2.

`\displaystyle\text{if}\quad G= (x-C)/(x)`


`x \\eq 0`

Multiply both sides by x:


`Gx=x-C`

Subtract from both sides Gx:


`x-C-Gx=0`

Then solve this equation:


`\displaystyle x-Gx-C=0\\x(1-G)=C\\x= (C)/(1-G)`