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\frac{2\sqrt{x-3}}{2}=\frac{6}{2}
Divide both sides by 2.
\sqrt{x-3}=\frac{6}{2}
Dividing by 2 undoes the multiplication by 2.
\sqrt{x-3}=3
Divide 6 by 2.
x-3=9
Square both sides of the equation.
x-3-\left(-3\right)=9-\left(-3\right)
Add 3 to both sides of the equation.
x=9-\left(-3\right)
Subtracting -3 from itself leaves 0.
x=12
Subtract -3 from 9.