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You need the pythagorean theorem to solve this, but you also need to know how to multiply binomials.
The short leg is X, the longer leg is (2X - 2) and the hypotenuse is (2X + 2).
We know the pythagorean theorem:
leg^2 + leg^2 = hypotenuse^2
So, in this case:
X^2 + (2X - 2)^2 = (2X + 2)^2
The next step is to expand the binomials. Take each part of the first one and multiply it against each part of the second one.
(2X - 2)(2X - 2) = 4X^2 - 4X - 4X + 4
= 4X^2 - 8X + 4
Then on the other side:
(2X + 2)(2X + 2) = 4X^2 + 4X + 4X + 4
= 4X^2 + 8X + 4
String it all together, and you get this:
X^2 + 4X^2 - 8X + 4 = 4X^2 + 8X + 4
You can combine the first two elements on the left, to get:
5X^2 - 8X + 4 = 4X^2 + 8X + 4
Now you just need to simplify this. First, subtract 4 from each side. That leaves you with:
5X^2 - 8X + 4 - 4 = 4X^2 + 8X + 4 - 4
5X^2 - 8X = 4X^2 + 8X
Next, get rid of the -8X on the left by adding 8X to each side.
5X^2 - 8X + 8X = 4X^2 + 8X + 8X
5X^2 = 4X^2 + 16X
You should see the process by now. I think you can finish simplifying this equation. Start by subtracting 4X^2 from each side!!! Good luck!
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