Can anyone help with this Algebra problem?

👨🏻‍🏫 學術台數學

[匿名]

2009-06-27 6:55 am

It's the pythagorean theorem.

(x-4)^2 + (12)^2 = x^2

x = 20, but I don't know how to find it.

更新1:

I'm lost at 8x. I thought (x-4)^2 would be .. x^2+16 Plus the 144, all equaling to x^2 .. But then I cant solve it that way. So what am I doing wrong. I got everything you guys did, but I don't really understand how you got to the distributing of the ^2 and everything after that. I think I'm missing something ..

更新2:

Thanks Todd! I got it.

回答 (8)

[匿名]

2009-06-27 7:04 am

✔ 最佳答案

first solve the part with the numbers... so 12^2 = 144. then factor, or foil out the (x-4)^2 part... to get x^2-8x+16.

now all together you have x^2-8x+16+144=x^2. combine the numbers 16+144 = 160.
now you have x^2-8x+160 = x^2.

Now solve to get the x by itself... take one of the x^2 and subtract it from the other side... they end up cancelling out. now you have..

-8x+160=0, to get the x by itself we move the 160 to the other side by subtracttion since its a positive number. now you have...
-8x=-160.

now to get the x by itself, divide each side by -8 and you get x=20.

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[匿名]

2009-06-27 2:01 pm

FOIL the (x-4) term.
(x-4)^2 + (12)^2 = x^2 ----> x^2-8x+16 + 144 = x^2

the x^2 terms cancel each other out and you're left with 8x = 160

therefore x = 20

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An ESL Learner

2009-06-27 2:42 pm

(x - 4)^2 + 12^2 = x^2
(x - 4)(x - 4) + 12(12) - x^2 = 0
x(x) - x(4) - 4(x) + 4(4) + 144 - x^2 = 0
x^2 - 4x - 4x + 16 + 144 - x^2 = 0
x^2 - x^2 - 8x + 160 = 0
-8x = -160
x = -160/(-8)
x = 20

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[匿名]

2009-06-27 2:14 pm

ok this is goin to be hard to explain on the computer.

1.) foil (x-4)^2, (x-4)(x-4), x^2-8x+16, and 12^2 is 144
so, x^2-8x+16+144=x^2
2.) at like terms
so, x^2-8x+160=x^2
3.) isolate x by subtracting x^2 from both sides
so, -8x+160=0
subtract 160 from both sides
so, -8x=-160
divide both sides by -8
so x=20

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nozar nazari

2009-06-27 2:06 pm

x^2+16-8x-x^2+144=0
160-8x=0
x=20

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[匿名]

2009-06-27 2:03 pm

well first multiply (x-4)^2 out so its x^2-8x+16
then put the whole leftside of the equation together so its:
x^2-8x+160=x^2

then set the left side equal to zero so it's: -8x+160=0
now move the x to one side and the numbers to the other so it's:
8x=160 and finally...solve for x
160/8=20 so x=20
hope this helped :)

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[匿名]

2009-06-27 1:59 pm

(x-4)^2 + (12)^2 = x^2

x^2-8x+16+144=x^2

-8x+16+144=0

-8x=-160
x=20

👍 0 👎 1

[匿名]

2009-06-27 1:59 pm

(x-4)^2 + (12)^2 = x^2

x^2 - 8x + 16 + 144 = x^2
-8x + 160 = 0
8x = 160
x = 20

👍 0 👎 1

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