coordinates

Isolate the constant: $2x^2 + 2y^2 + 10x - 6y = 18$

Divide the entire equation by 2: $x^2 + y^2 + 5x - 3y = 9$

Add $8.5$ to both sides so we can complete the square for both x and y: $x^2 + y^2 + 5x - 3y +8.5= 17.5$

Complete the square: $(x+2.5)^2 + (y - 1.5)^2 = 17.5$

Note the constant on the left-hand side equals the radius of the circle squared, meaning the area of the circle is $\color{brown}\boxed{17.5 \pi}$