Question 741096
x = side length of the smaller tile

1728*x^2 represents the area of this floor.


The other tile sized at x+2, covered that same area and this area expressible as 432*(x+2)^2 using these larger tiles.


Same area!   {{{1728x^2=432(x+2)^2}}}.
Find x.  



Plenty of ways to make mistakes in solving that equation.  Misfactoring, transposing an incorrect number, sign mistake,...



{{{1728x^2=432(x+2)^2}}}
{{{4x^2=(x+2)^2}}}
{{{4x^2=x^2+4x+4}}}
{{{3x^2-4x-4=0}}},  factorable, but,....


{{{x=(4+sqrt(16-4*3*(-4)))/(2*3)}}}, direct use of quadratic formula solution
{{{x=(4+8)/(6)}}}
{{{highlight(x=2)}}}



For factoring starting from the simplified quadratic equation,
{{{3x^2-4x-4=(3x+2)(x-2)=0}}}
Take the positive root, {{{x=2}}}.