Thread: How do I get these equations into the form of a quadric surface equation?

A question in my text asks to classify the surfaces by comparing them with the standard equations of quadric surfaces. My problem is I can't figure out how to get these equations into the standard form of quadric surface equations. Can someone please tell me the answer to this and explain how to do it? Thanks in advance.

surface 1:

surface 2:

Rewrite

x^2 +3x +2*y^2 -z^2 =1

Complete the square:

(x+3/2)^2 + 2y^2 -z^2 = 13/4

which is a hyperboloid of one sheet

recall to complete the square ax^2 +bx = a(x+b/2a)^2 - b^2/4a

In the second problem complete the square in y