Question

Buried treasure. Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x+6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x+4 paces to the east. If they share their information, then they can find x and save a lot of digging. What is x?
Pythagorean Quadratic problem. Can some one please tell me if I set this problem up correct?
x^2+(2x+4) = (2x+6)^2

Answer 1

your set up is close, but it's incorrect unfortunately

Answer 2

it should be this

x^2+(2x+4)^2 = (2x+6)^2

notice how the "(2x+4)" is squared

Answer 3

How about is the next step correct? x^2+4x^2+16x+16=4x^2+24x+36

Answer 4

yes it is, keep going

Answer 5

-4x^2 -4x^2
x^2+16x+16=24x+36
-24x -24x
x^2-8x+36=36
-36 -36
x^2-8x-0+0

Answer 6

close

Answer 7

here's what I'm getting

Answer 8

x^2+(2x+4)^2 = (2x+6)^2


x^2+(2x+4)(2x+4) = (2x+6)(2x+6)


x^2+2x(2x+4)+4(2x+4) = 2x(2x+6)+6(2x+6)


x^2+4x^2+8x+8x+16 = 4x^2+12x+12x+36


5x^2+16x+16 = 4x^2+24x+36


5x^2+16x+16 - 4x^2-24x-36 = 0


x^2-8x-20 = 0

Answer 9

How did you get the 20

Answer 10

16 - 36 = -20

Answer 11

on the left side, you had 16, but it somehow changed to 36

Answer 12

Did I skip steps/

Answer 13

Ok I got you. I see. x^2-8x-20 so now I need two factors of 20 that add up to 8?

Answer 14

-20 and -8, but yes

Answer 15

5*4 =20, 5+4=9, 2*10=20, 2+10 =12, 10+10=20 I have no idea

Answer 16

how about -10 and 2

Answer 17

-10 + 2 = -8

-10 * 2 = -20

Answer 18

ok, wasn't thinking of the negatives. (x-10)(x+8)?

Answer 19

good

Answer 20

oh sry misread

Answer 21

it should be (x-10)(x+2)

Answer 22

(x-10)(x+2) that is what I meant sorry

Answer 23

so if

x^2-8x-20 = 0

then

(x-10)(x+2) = 0

Answer 24

and if

(x-10)(x+2) = 0

then by the zero product property

x-10 = 0 or x+2 = 0

Answer 25

that is far as we can go?

Answer 26

no we can go a few steps further

Answer 27

we need to fully isolate x

Answer 28

Ok, we haven't got that far yet, but will you show me?

Answer 29

if x-10 = 0, then x = ???

Answer 30

0

Answer 31

no

Answer 32

if x-10 = 0, then x = ???

Answer 33

I0

Answer 34

better

Answer 35

if x+2 = 0, then x = ???

Answer 36

-2

Answer 37

so this means we have these 4 steps at the end


x^2-8x-20 = 0


(x-10)(x+2) = 0


x-10 = 0 or x+2 = 0


x = 10 or x = -2

Answer 38

but remember that x is a distance or length

you CANNOT have negative distances or lengths, so x = -2 makes no sense in the real world

Answer 39

so that means we must toss x = -2

therefore, the only solution is x = 10

Answer 40

okay, thank you very much for your patience. May the Lord God Bless you, you have helped me greatly.

Answer 41

you're welcome, glad to be of help