Question 798780
Let {{{ x }}} = the width
{{{ x + 3 }}} = the length
{{{ x*( x+ 3 ) = 54 }}}
{{{ x^2 + 3x = 54 }}}
You can solve this by completing the square
{{{ x^2 + 3x + (3/2 )^2 = 54 + (3/2)^2 }}}
{{{ x^2 + 3x + 9/4  =  216/4 + 9/4}}}
{{{ x^2 + 3x + 9/4 = 225/4 }}}
{{{ ( x + 3/2 )^2 = ( 15/2 )^2 }}}
{{{ x + 3/2 = 15/2 }}}
{{{ x = 15/2 - 3/2 }}}
{{{ x = 12/2 }}}
{{{ x = 6 }}}
and
{{{ x + 3 = 9 }}}
The dimensions are 6' x 9'
check:
{{{ x = 6 }}}
{{{ x - 6 = 0 }}}
also, there is a negative square root in the answer, too
{{{ x + 3/2 = -15/2 }}}
{{{ x = -18/2 }}}
{{{ x = -9 }}}
{{{ x + 9 = 0 }}}
So, the factors are:
{{{ ( x - 6 )*( x + 9 ) = 0 }}}
{{{ x^2 - 6x + 9x - 54 = 0 }}}
{{{ x^2 + 3x = 54 }}}
{{{ x*( x + 3 ) = 54 }}}
This is the original equation