Word problem help please

[ktkeiper]

I set this problem up and tried to solve it using both the quadratic formula and completing the square - I got the same answer both times, but I'm not sure I even set it up right... Could you go through my work and see if you catch any mistakes, please?

Martha's garden is 5m wide and 8m long. Next year she plans to double the garden's area by increasing the width and length by the same number of meters. What will the new dimensions of the garden be?

80=(5+x)(8+x)
80=x^2+13x+40
x^2+13x+42.25=82.25
(x+6.5)^2=82.25
x+6.5=9.07,-9.07
x=-6.5+9.07, -6.5-9.07
x=2.57,-15.57
(since it can't be negative, I took out -15.57)
The garden will be 7.57m by 10.57 m

 

[ktkeiper]

I am not sure why you doubt yourself. A garden with dimensions of exactly 7.57 by 10.57 has an area of 80.0149, which admittedly differs from 80 by 0.0149. But the square root of 82.25 is not exactly 9.07. If you use the more accurate 9.069, you will come up with dimensions of 7.569 and 10.569 and an area of 79.9968, which differs from 80 by 0.0032.

Because I have a migraine and didn't know if I actually solved it the right way. I've solved things the wrong way before and still gotten the correct answer, but since my teachers take off points if the work is incorrect for word problems, I thought I'd better double check. Thank you!