area=LW
54=LW
L is 2 more than x L=2+x
w is 5 less than 2x W=-5+2x
54=LW
L=2+x
W=-5+2x
input
54=(2+x)(-5+2x)
distribute/FOIL
54=-10+4x-5x+2x^2
add like terms
54=-10-x+2x^2
minus 54
2x^2-x-64=0
quadratic formula
x=[tex] \frac{ -b+/-\sqrt{b^{2}-4ac} }{2a} [/tex]
x=[tex] \frac{ -(-1)+/-\sqrt{(-1)^{2}-4(2)(-64)} }{2(2)} [/tex]
x=[tex] \frac{ 1+/-\sqrt{1-(-256)} }{4} [/tex]
x=[tex] \frac{ 1+/-\sqrt{1-(-256)} }{4} [/tex]
x=4.257 or -3.75
we disregard the negative one because that would make legnth and width negative
x=4 (rounded)
