Question 617026
A generic quadratic equation would be {{{ax^2+bx+c=0}}}
We solve it by isolating the terms with x on one side of the equal sign and "completing the square".
Then we "unsquare" the completed square by taking square roots on both sides and adding the plus/minus options.
You can always do it in an equation with numbers coefficient,
but doing it with generic a, b, and c coefficients leads to the infamous quadratic formula.
{{{ax^2+bx+c=0}}} --> {{{ax^2+bx+c-c=0-c}}} --> {{{ax^2+bx=-c}}} --> {{{(ax^2+bx)/a=-c/a}}} --> {{{x^2+(b/a)x=-c/a}}} --> {{{(x+(b/a)x+(b/2a)^2)=(b^2/4a^2)-c/a}}}
So {{{x+b/2a=sqrt((b^2-4ac)/4a^2)=sqrt(b^2-4ac)/2a}}} or {{{x+b/2a=sqrt((b^2-4ac)/4a^2)=-sqrt(b^2-4ac)/2a}}}
In sum:
{{{x=-b/2a +- sqrt((b^2-4ac)/4a^2)=-b/2a +- sqrt(b^2-4ac)/sqrt(4a^2)=-b/2a +- sqrt(b^2-4ac)/2a=(-b +- sqrt(b^2-4ac))/2a}}}