Question 131658
If the original side length is x, then the new side length must be x + 4.  The area of a square is the length of the side squared, so


{{{(x+4)^2=100}}}


{{{x^2+8x+16=100}}}


{{{x^2+8x-84=0}}}


{{{-6 * 14 = -84}}} and {{{-6+14=8}}}, so


{{{(x-6)(x+14)=0}}}


So {{{x=6}}} or {{{x=-14}}}.  Since we are looking for a measure of length, -14 doesn't make sense, so we can exclude this root as extraneous caused by squaring the variable.  The original length of the side of the garden is then 6 meters.


Check the answer:  {{{6+4=10}}}, {{{10^2=100}}}