### Home > A2C > Chapter 8 > Lesson 8.2.3 > Problem 8-149

8-149.

Complete the square to change 3*x*^{2} + 6*x* + 3*y*^{2} − 18*y* − 45 < 0 to graphing form. Identify key points. Find the domain and range. Sketch the graph. Homework Help ✎

3(*x*^{2} + 2*x*) + 3(*y*^{2} − 6*y*) − 45 < 0

3(*x* + 1)^{2} + 3(*y* − 3)^{2} − 75 < 0

Divide by 3, then simplify.

(*x* + 1)^{2} + (*y* − 3)^{2} < 25

Center = (−1, 3)

Radius = √25 = 5

Domain = −6 < *x* < 4

Range = −2 < *y* < 8