Question 834971
The two bottom dimensions are (22-2x) and (34-2x).  The height dimension is x.
Volume of this box is {{{x(22-2x)(34-2x)=700}}},
{{{4x(11-x)(17-x)=700}}}
{{{4x(187-11x-17x+x^2)=700}}}
{{{4x(187-28x+x^2)=700}}}
{{{x(x^2-28x+187)=175}}}
{{{highlight_green(x^3-28x^2+187x-175=0)}}}


Two best choices to solve the equation are either Rational Roots Theorem, or use a graphing calculator to find the zeros.  I am not continuing this UNLESS you want that help.