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Question

What are  and  for         written as      ?

  

  

Answer 1

The technique for solving this is called "completing the square".

Recognize that (x - p)² = x² - 2px + p²

Since the given equation begins with 2x² , we first need to divide everything by 2 to get:

x² + 3x/2 + 4 = 0 <----equation 1

From the 1st 2 terms, we can see that p = -3/4. We can now write:

(x - (-3/4))² =

x² + 3x/2 + 9/16

To make this match equation 1, put -4 +9/16 on the right to get:

x² + 3x/2 + 9/16 = - 55/16

In the specified format:

(x + 3/4)² = -55/16

thus p = -3/4, and q = -55/16

<<Edited to correct the mistake flagged by David W---it looks like the answer is still right>>