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

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Homework Help Overview

The problem involves rewriting the quadratic equation 3x^2 + 12x + 5 in the form p(x + q)^2 + r, with the goal of finding the values of p, q, and r. The subject area is algebra, specifically focusing on quadratic equations and completing the square.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use the method of completing the square but expresses confusion about the process and the correct steps to take. Some participants suggest rewriting the quadratic expression directly and comparing it to the desired form. Others emphasize the importance of not dividing by the leading coefficient initially and propose factoring out a common factor from the first two terms.

Discussion Status

The discussion is ongoing, with participants providing hints and guidance on how to approach the problem of completing the square. Multiple interpretations of the problem-solving steps are being explored, and there is a focus on clarifying the method rather than reaching a final solution.

Contextual Notes

The original poster indicates a lack of understanding of the problem, which may be affecting their ability to proceed. There is also a mention of the need for clearer explanations, particularly for those who are new to the topic.

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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.
 
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Try to rewrite [tex]3x^2 + 12x +5[/tex] itself using completing the square, then compare the result to [tex]p(x+q)^2 + r[/tex]
 
statdad said:
Try to rewrite [tex]3x^2 + 12x +5[/tex] itself using completing the square, then compare the result to [tex]p(x+q)^2 + r[/tex]

I'm sorry you have to be more clear, I'm a newb.
 
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).
 
Start with [itex]3x^2+12 + 5[/itex], write it as [itex]3(x^2+4x) + 5[/itex], and complete the square to write it as [itex]3(x+ \text{something })^2 + \text{something}[/itex].

Then compare it with [itex]p(x+q)^2 + r[/itex].
 

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