Answer:
feet length = 2x – 3 feet; width = x + 2 feet
Step-by-step explanation:
we have
The area of a rectangular garden in square feet is
[tex]A=2x^{2}+x-6[/tex]
Remember that
The area of a rectangular garden is
[tex]A=LW[/tex]
where
L is the length and W is the width
Convert the equation in factored form
[tex]2x^{2}+x-6=0[/tex]
[tex]2x^{2}+x=6[/tex]
Factor the leading coefficient
[tex]2(x^{2}+0.5x)=6[/tex]
Complete the square
[tex]2(x^{2}+0.5x+1/16)=6+1/8[/tex]
[tex]2(x^{2}+0.5x+1/16)=49/8[/tex]
Rewrite as perfect square
[tex]2(x+1/4)^{2}=49/8[/tex]
[tex](x+1/4)^{2}=49/16[/tex]
square root both sides
[tex](x+1/4)=(+/-)(7/4)[/tex]
[tex]x=-1/4(+/-)(7/4)[/tex]
[tex]x=-1/4(+)(7/4)=3/2[/tex]
[tex]x=-1/4(-)(7/4)=-2[/tex]
so
[tex]2x^{2}+x-6=(x-3/2)(x+2)[/tex]
[tex]2x^{2}+x-6=(2x-3)(x+2)[/tex]
therefore
feet length = 2x – 3 feet; width = x + 2 feet
