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need help solving pythagorean quadratic...

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

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Dear Eric,
Next time, please, copy the problem exactly as it appear in the original source, and not your own interpretation.
2x+6 > 2x+4 , so the equation you gave us to solve does not match the description you wrote.

I gave the precise equation - x^2+(2x+6)^2=(2x+4)^2
This is to be factored, it also requires the use of the Pythagorean Theorem to solve it....
If it was relayed any differently, I don't recall my mistake...
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? This is the exact question.
Thanks

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2 Answers

so since you have (2x+4)^2 and (2x+6)^2. Your first job is to take this solve and uncoil these two expressions first.

(2x+4)^2 can be solved using the squared for formula. 

(a+b)^2 = (a^2 + 2*a*b + b^2) = (a+b) * (a+b) 

Therefore (2x+4)^2 = (2x)^2 + 2*2x*4 + (4)^2

                              = 4x^2 + 16x + 16

and Therefore (2x+6)^2 = (2x)^2 + 2*2x*6 + (6)^2

                                   = 4x^2 + 24x + 36

Now that those polynomials are taken cared we have to put all together in the solution:

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

Its better to put everything to one side and make it equal to zero.

so, x^2 + 4x^2 + 24x + 36 - (4x^2 +16x +16) = 4x^2 + 16x + 16 - ( 4x^2 + 16x + 16)

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

group the x^2 with each other and add them and do the same for the x's and the numbers.

so, x^2 + 4X^2 - 4x^2 + 24x - 16x + 36 -16 = 0

then you have, x^2 + 8x + 20 = 0 

Now solve this equation using factorization or the quadratic equation.

reply to this comment if you need further help. 

 

Comments

Thank you so much for your help Ataur, I see where I went wrong in my math. I now have to find two factors of 20 whose sum would equal the coefficient of 8, and there are none..
Can you help?

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(2x + 6)2 - x2 = (2x + 4)2
4x2 + 24x + 36 - x2 = 4x2 + 16x + 16
24x + 36 - x2 = 16x + 16
0 = x2 - 24x - 36 + 16x + 16
x2 - 8x - 20 = 0
x1 = (8 - √(64 + 80))/2 = -2 (does not satisfy given problem: distance can not be negative)
x2 = (8 + √(64 + 80))/2 = 10 , thus  x = 10

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You"re very welcome Eric.
Sorry for late answer, I solved it before I wrote the note for you, but for some reason the answer did not appear. There was a note "Your answer is accepted", but it did not go through completely.

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