Answer:
x=6
Step-by-step explanation:
Since this is a right triangle we can use the Pythagorean theorem
a^2 + b^2 = c^2
where a and b are the legs and c is the hypotenuse
x^2 + (x+2)^2 = (2x-2)^2
FOIL (x+2)^2 = x^2 +2x+2x+4 = x^2 +4x+4
FOIL (2x-2)^2 = 4x^2 -4x -4x+4 = 4x^2 -8x+4
Replacing these in to the equation
x^2 +x^2 +4x+4 = 4x^2 -8x+4
Combine like terms
2x^2 +4x +4 = 4x^2 -8x +4
Subtract 4 from each side
2x^2 +4x +4-4 = 4x^2 -8x +4-4
2x^2 +4x = 4x^2 -8x
Subtract 2x^2 from each side
2x^2 -2x^2+4x = 4x^2-2x^2 -8x
4x = 2x^2 -8x
Subtract 4x from each side
4x-4x = 2x^2 -8x-4x
0 = 2x^2 -12x
Factor out a 2x
0 = 2x(x-6)
Using the zero product property
2x =0 x-6 =0
x =0 x-6+6 = 0+6
x = 0 c=6
