Question 833965
Given:
l = 14
w = 8 then
a = 14*8 = 112
We want to add x meters to l and w to double the area, or
(1) (14+x)*(8+x) = 2*112 or
(2) 112 + 14x + 8x + x^2 = 224 or
(3) x^2 + 22x - 112 = 0
Use the quadratic solution equation
(4) {{{(-b+-sqrt(b^2-4*a*c))/(2*a)}}} to get
(5) {{{(-22+-sqrt(22^2-4*1*(-112)))/(2*1)}}}  or
(6) x = -26.264, 4.264
Using the positive value of x for the number of meters to add to the original rectangular dimensions to get
(7) A = (14+4.264)*(8+4.264) or
(8) A = 223.996
Answer: Add 4.3 meters (nearest tenth) to each of the rectangular dimensions.