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\sqrt{x-2}+|y-4|-|y-4|=-|y-4|
Subtract |y-4| from both sides of the equation.
\sqrt{x-2}=-|y-4|
Subtracting |y-4| from itself leaves 0.
x-2=\left(y-4\right)^{2}
Square both sides of the equation.
x-2-\left(-2\right)=\left(y-4\right)^{2}-\left(-2\right)
Add 2 to both sides of the equation.
x=\left(y-4\right)^{2}-\left(-2\right)
Subtracting -2 from itself leaves 0.
x=\left(y-4\right)^{2}+2
Subtract -2 from \left(y-4\right)^{2}.