SOLUTION: Can you please explain the steps and how I would solve x^2 + (2x + 4)^2 = (2x + 6)^2 using the Pythagorean theorem?

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Question 779012: Can you please explain the steps and how I would solve
x^2 + (2x + 4)^2 = (2x + 6)^2 using the Pythagorean theorem?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+%282x+%2B+4%29%5E2+=+%282x+%2B+6%29%5E2....using the Pythagorean theorem a%5E2%2Bb%5E2=c%5E2, means we have right angle triangle where side x=a, side b=%282x+%2B+4%29, and hypotenuse c=%282x+%2B+6%29
so, first find x
x%5E2+%2B+%282x%29%5E2+%2B16x%2B4%5E2+=+%282x%29%5E2+%2B24x%2B+6%5E2
x%5E2+%2B+4x%5E2+%2B16x%2B16+=4x%5E2+%2B24x%2B+36...simplify
x%5E2+%2Bcross%28+4x%5E2%29+%2B16x%2B16+=cross%284x%5E2%29+%2B12x%2B+36
x%5E2+%2B16x%2B16+=24x%2B+36
x%5E2+%2B16x%2B16-24x-36=0
x%5E2-8x-20=0.....use quadratic formula to find x
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%2A1%2A%28-20%29+%29%29%2F%282%2A1%29+
x+=+%288+%2B-+sqrt%28+64%2B80+%29%29%2F2+
x+=+%288%2B-+sqrt%28+144%29%29%2F2+
x+=+%288%2B-+12%29%2F2+
solutions:
x+=+%288+%2B+12%29%2F2+
x+=+20%2F2+
x+=+10+
or
x+=+%288+-+12%29%2F2+
x+=+-4%2F2+
x+=+-2+
now, if we need to find the length of sides, we will use only positive solution
x+=+10+

x=a=> a=10+
b=%282x+%2B+4%29=>b=%282%2A10+%2B+4%29=> b=24
c=%282x+%2B+6%29=>c=%282%2A10+%2B+6%29=>c=26
check:
a%5E2%2Bb%5E2=c%5E2
10%5E2%2B24%5E2=26%5E2
100%2B576=676
676=676