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## need help solving pythagorean quadratic...

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

Am I going to get an answer?

Any help would be appreciated.

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

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.

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?

(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