Question 252222
{{{A = xy - (1 - z/4)r^2}}} Start with the given equation.



{{{A - xy = - (1 - z/4)r^2}}} Subtract xy from both sides.



{{{(A - xy)/(-(1 - z/4)) = r^2}}} Divide both sides by {{{- (1 - z/4)}}}.



{{{-(A - xy)/(1 - z/4) = r^2}}} Reduce.



{{{sqrt(-(A - xy)/(1 - z/4)) = r}}} Take the square root of both sides. Note: Since 'r' is positive, we don't have to worry about the negative square root.



So the answer is {{{r=sqrt(-(A - xy)/(1 - z/4))}}}



Note: if the original problem was {{{A = xy - ((1 - z)/4)r^2}}}, then the answer is {{{r=sqrt(-(A - xy)/((1 - z)/4))}}} which simplifies to {{{r=sqrt(-(4(A - xy))/(1 - z))}}}