A rectangular piece of land measures 20 feet by 15 feet. James created a cement sidewalk, x feet wide, to border a rectangular garden on all four sides as shown below. If the garden has an area of 150 square feet, how wide is the sidewalk?
A
12.25 feet

B
6.12 feet

C
5 feet

D
2.5 feet

The second and fourth answer are correct

Step-by-step explanation:

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81