Answer:
The garden can not have area of 700ft^2
Step-by-step explanation:
We are given equation for area as
[tex]A(w)=w\times (50-w)[/tex]
where
w is the width (in feet) of the garden
now, we are given area =700 ft^2
so, we can set area =700
and then we can solve for w
[tex]w\times (50-w)=700[/tex]
[tex]50w-w^2=700[/tex]
[tex]-w^2+50w-700=0[/tex]
now, we can use quadratic formula
[tex]ax^2+bx+c=0[/tex]
[tex]w=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
we can compare and find a,b, and c
a=-1 , b=50 , c=-700
now, we can plug values
[tex]w=\frac{-50\pm \sqrt{50^2-4\left(-1\right)\left(-700\right)}}{2\left(-1\right)}[/tex]
[tex]w=25-5\sqrt{3}i,\:w=25+5\sqrt{3}i[/tex]
We can see that values of w is not real
so, w does not exists when area =700
so, The garden can not have area of 700ft^2
