Question 980216
x=9+y for length with width y.
Area is {{{(9+y)*y=A}}}.


New rectangle,
{{{2(9+y)(y+4)=(A+138)}}}----OBVIOUS MISTAKE MADE HERE.
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Simplify this new rectangle equation.
{{{2(y+9)(y+4)=A+138}}}
{{{2(y^2+13y+36)-A-138=0}}}
{{{2y^2+26y+72-a-138=0}}}
{{{2y^2+26y-A-66=0}}}
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What to do next, is substitute for A using the original area equation.
{{{2y^2+26y-(y^2+9y)-66=0}}}
{{{2y^2+26y-y^2-9y-66=0}}}
{{{y^2+17y-66=0}}}
{{{(y-6)(y+11)=0}}}
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The meaningful value for *y is {{{highlight(y=6)}}}.
*{{{x=y+9=6+9=highlight(15=x)}}}.
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*Those are wrong, because of the noted OBVIOUS MISTAKE.
New rectangle width should be y-4, not y+4.



DONE CORRECTLY, THIS IS HOW THE STEPS GO:
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{{{system(x=y+9, y(y+9)=A)}}}


NEW:  {{{2(y+9)(y-4)=A+138}}}
{{{2(y^2+5y-36)=A+138}}}
{{{2y^2+10y-72-138-A=0}}}
{{{2y^2+10y-y^2-9y-72-138=0}}}
{{{2y^2+10y-y^2-9y-210=0}}}
{{{y^2+y-210=0}}}
{{{(y-14)(y+15)=0}}}
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{{{highlight(y=14)}}}
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Returning to {{{x=y+9}}}
{{{x=14+9}}}
{{{highlight(x=23)}}}