Question 388836
You end up subtracting 2 in. from each side.
Call the length of the sheet {{{x}}}
The width of the sheet is then {{{x - 5}}}
After cutting out the 1 inch squares from the 
corners, the length is {{{x - 2}}} and the 
width is {{{x - 7}}}
{{{V = 1*(x - 2)*(x - 7)}}}
{{{V = x^2 - 9x + 14}}}
And, if {{{V = 30}}} in.
{{{30 = x^2 - 9x + 14}}}
{{{x^2 - 9x - 16 = 0}}}
Using the quadratic equation:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{a = 1}}}
{{{b = -9}}}
{{{c = -16}}}
{{{x = (-(-9) +- sqrt( (-9)^2-4*1*(-16) ))/(2*1) }}} 
{{{x = (9 +- sqrt( 81 + 64 ))/2 }}} 
{{{x = (9 +- sqrt( 145 ))/2 }}}
{{{x = (9 + 12.042)/2}}}
{{{x = 21.042/2}}}
{{{x = 10.52}}}
{{{x - 5 = 5.52}}}
{{{x - 2 = 8.52}}}
{{{x - 7 = 3.52}}}
The dimensions of the cardboard are 5.52 x 10.52 in2
check:
The volume would be {{{1*8.52*3.52 = 29.99}}}
This looks close enough