(10 -√75) / 5
(10 - √25*3) / 5
(10 - 5√3) / 5
(10*2 - 5*2√3)/5 <============ THIS IS WHERE I GET LOST
Why did you multiply the numerator by 2?
If you had written this as an equation, your error would have been apparent.
[MATH](10 - \sqrt{75}/5 = x\implies [/MATH]
[MATH](10 - \sqrt{25 * 3})/5 = x \implies[/MATH]
[MATH](10 - 5\sqrt{3})/5 = x \implies [/MATH]
[MATH]2(10 - 5\sqrt{3})/5 = 2x \implies[/MATH]
[MATH](20 - 10\sqrt{3})/5 = 2x \implies[/MATH]
[MATH]4 - 2\sqrt{3} = 2x.[/MATH]
Now divide by 2 to get the correct answer
[MATH](4 - 2\sqrt{3})/2 = 2x/2 \implies [/MATH]
[MATH]x = 2 - \sqrt{3}.[/MATH]
Your multiplying by 2 led you astray. Why did you think it was helpful?