L=6+W
A=LW
sub 6+W for L
A=(6+W)(W)
expand
oh, A=50
50=W²+6W
minus 50 both sides
0=W²+6W-50
we gots to use quadratic formula
for
aW²+bW+c=0
W=[tex] \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
we got
a=1
b=6
c=-50
W=[tex] \frac{-(6)+/- \sqrt{(6)^2-4(1)(-50)} }{2(1)} [/tex]
W=[tex] \frac{-6+/- \sqrt{36+200} }{2} [/tex]
W=[tex] \frac{-6+/- \sqrt{236} }{2} [/tex]
W=[tex] \frac{-6+/- 2\sqrt{59} }{2} [/tex]
W=[tex] -3+/- \sqrt{59} [/tex]
W=[tex] -3+ \sqrt{59} [/tex] or W=[tex] -3- \sqrt{59} [/tex]
aprox
W=-10.6811 or W=4.68115
can't be negative width
width=4.68115 or -3√59
