Question 989463
Volume of the new box:
{{{(3+x)(5+x)8}}},  34 cubic cm more volume than the old box.


{{{(x+3)(x+5)*8-3*5*8=34}}}


{{{(x^2+8x+15)*8-120-34=0}}}
{{{(x^2+8x+15)*8-154=0}}}
{{{(x^2+8x+15)*4-77=0}}}
{{{4x^2+32x+60-77=0}}}
{{{4x^2+32x-17=0}}}


Try directly using formula for general solution of quadratic equation to find x.

Discriminant is  ....,  {{{36^2}}}.


{{{x=(-32+36)/(2*4)}}}
{{{highlight(x=1/2)}}}
Find the new dimensions from this.