What are the values of p, q, and r in this quadratic equation?

[AD7863]

Homework Statement

Given that for all values of x:

3x^2 + 12x + 5 = p(x +q)^2 + r

a) find the values of p, q and r
b) solve the equation 3x^2 + 12x + 5 = 0

The Attempt at a Solution

I'm completely lost here but here's my attempt at a solution - I'm pretty sure that I did it all wrong:

I divided them by 3 and moved the last bit to the other side of the equal sign and made it a minus. I tried using the complete the square method:

x^2+4x=-7/3

After that I have no idea what to do... I don't have a clue how I find the values of p, q and r.

 

[statdad]

Try to rewrite $$3x^2 + 12x +5$$ itself using completing the square, then compare the result to $$p(x+q)^2 + r$$

 

[AD7863]

Try to rewrite $$3x^2 + 12x +5$$ itself using completing the square, then compare the result to $$p(x+q)^2 + r$$

I'm sorry you have to be more clear, I'm a newb.

 

[eumyang]

In other words, don't divide by 3 first. It is possible to complete the square even if the coefficient of the x² term is not 1. Here's a hint to get you started: factor out a GCF from the first 2 terms only (ignoring the constant term).

 

[statdad]

Start with $3x^2+12 + 5$, write it as $3(x^2+4x) + 5$, and complete the square to write it as $3(x+ \text{something })^2 + \text{something}$.

Then compare it with $p(x+q)^2 + r$.