Question 286471
Since b is somewhere on ac, this means that {{{ab+bc=ac}}} by the segment addition postulate (ie the parts of a line segment add up to the total line segment)


So {{{6x+x^2=27}}} which then becomes {{{x^2+6x-27=0}}}. Factor to get {{{(x+9)(x-3)=0}}}. Now use the zero product property and solve to get {{{x=-9}}} or {{{x=3}}}



Since we're dealing with lengths, the only sensible answer is {{{x=3}}}