# Help please this is giving me trouble?

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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 ...show more

Best Answer

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

(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

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