Question

Josephine has a rectangular garden with an area of 2x2 + x – 6 square feet

Answer 1

Factor
2x^2+x-6
trial and error, the factors are the legnth and width
or, we could try multiplying the given options
if we do we find the factored form is
(x+2)(2x-3)
answer is last one

Answer 2

we have

$2x^{2} +x-6$

we know that

The area of a rectangle is equal to

$A=L*W$

where

L is the length side of the rectangle

W is the width side of the rectangle

In this problem

Equate the area to zero and Find the roots of the quadratic equation

$2x^{2} +x-6=0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$2x^{2} +x=6$

Factor the leading coefficient

$2(x^{2} +0.5x)=6$

Complete the square. Remember to balance the equation by adding the same constants to each side

$2(x^{2} +0.5x+0.25^{2})=6+0.125$

$2(x^{2} +0.5x+0.0625=6.125$

Rewrite as perfect squares

$2(x+0.25)^{2}=6.125$

$(x+0.25)^{2}=3.0625$

Square root both sides

$(x+0.25)=(+/-)\sqrt{3.0625}$

$(x+0.25)=(+/-)1.75$

$x1=-0.25+1.75=1.50$

$x2=-0.25-1.75=-2$

so

$2x^{2} +x-6=2(x+2)(x-1.50)$

$2(x+2)(x-1.50)=(x+2)(2x-3)$

$length=(2x-3)\ feet$

$width=(x+2)\ feet$

therefore

the answer is the option

$length=(2x-3)\ feet$ ; $width=(x+2)\ feet$