Help please this is giving me trouble?

Question

number 1.
Megan’s backyard has a small pond that is 15 feet by 10 feet. Her mother wants her to add a wooden deck pathway around the pond, so that the total area of the pool and deck is 234 ft2. How wide does the pathway need to be to fulfill Megan’s mom’s request?



number 2.
Part 1: Solve the following quadratic equation using one of the methods listed below.
Part 2: Using complete sentences, explain why you chose the method you used.

Equation:
0 = x2 + 6x + 3

Methods:
Completing the Square
Factoring
Quadratic Formula
Graphing

even if you only know how to do one of them please help !

Answer 1

Best Answer - Chosen by Voters

area is length x width and we are given that the pond is 10 x 15 so if we imagine that as a rectangle we know we must add some currently unknown amount so call it x to each of the for sides. we can write this as

(10 + 2x)(15 + 2x) (the original amount with an additional x for each side)

we are also told that this will equal 234 so

(10 + 2x)(15 + 2x) = 234 expand

4*x^2+50*x+150=234 subtract 234 from both sides

4*x^2+50*x-84=0 factor out a 2

2(2*x^2+25*x-42)=0 factor the rest

2(2x-3)(x+14)=0

2x-3=0 -> x=1.5 or x+14=0 -> x =-14

a negative dimension doesn't make any sense so throw it out and go with 1.5

and to check

(10 + 1.5 +1.5) * (15 + 1.5 +1.5) -> 13 * 18 = 234 check

so the path should be 1.5 feet wide

for the next one I'll do complete the sq as it wont factor easily and not everyone has a graphing calculator and it's just mighty fun

x^2 +6x +3 =0 subtract 3 from both sides

x^2 +6x = -3

To complete the square you divide the coefficient (number in front of) the second term by 2 and square it so in this case 6/2 = 3, 3^2= 9 and add that to both sides

x^2 +6x +9 = -3 +9

x^2 +6x +9 = 6

now since we completed the square it can be written as a perfect square like this

(x+3)^2 =6 take the sqrt of both sides

x+3 = sqrt(6) subtract 3 from both sides

x = -3 +/-sqrt(6)

remember that it's -3 plus the sqrt(6) AND -3 minus the sqrt(6) because 2^2=4 and -2^2 =4 and we have to account for both possibilities

hope that helps