Question 204020
I'll start where you're starting to get confused



{{{x=(8+-sqrt(124))/(10)}}} Start with the given equation.



The goal now is to simplify the right side any way we can. It turns out that the square root can be simplified.



{{{x=(8+-sqrt(4*31))/(10)}}} Factor 124 into 4*31. Note: 4*31=124. 



Why did we do this? Because when we break up the root, we can take the square root of 4 to get 2...


{{{x=(8+-sqrt(4)*sqrt(31))/(10)}}} Break up the square root.



{{{x=(8 +- 2*sqrt(31))/(10)}}} Take the square root of 4 to get 2.



{{{x=(2(4+-sqrt(31)))/(10)}}} Factor out the GCF 2 from the numerator.



{{{x=(2(4+-sqrt(31)))/(2*5)}}} Factor the denominator 10 to get 2*5



{{{x=(highlight(2)(4+-sqrt(31)))/(highlight(2)*5)}}} Highlight the common terms.



{{{x=(cross(2)(4+-sqrt(31)))/(cross(2)*5)}}} Cancel out the common terms.



{{{x=(4+-sqrt(31))/5}}} Simplify



So the solutions are {{{x=(4+sqrt(31))/5}}} or {{{x=(4-sqrt(31))/5}}} (since the 'plus/minus' breaks the equation in two).



Note: I showed more steps than you would necessarily show to illustrate what is really going on.