Posted by **Marysvoice** on Friday, February 15, 2008 at 7:31am.

What are the pros and cons of completing the square as a way to solve quadradic equations?

- Algebra Quadratic Equations -
**Guido**, Friday, February 15, 2008 at 8:02am
Completing the square is not the easiest way to solve quadratic equations; its strength lies in the fact that the process is repetitive and predictable.

Here is the best news: completing the square ALWAYS (SAY ALWAYS) will work, unlike the factoring method, which of course, requires that the trinomial be factorable.

- Algebra Quadratic Equations -
**Marysvoice**, Friday, February 15, 2008 at 9:28am
Thank you.

- Algebra Quadratic Equations -
**drwls**, Friday, February 15, 2008 at 8:15am
I find the quadratic equation

x = [-b +/- sqrt(b^2-4ac)]/2a

the easiest to use, unless a way of factoring is obvious. It is derived by completing the square, after all. It tells you the number of real roots right away (from the value of b^2 - 4ac). The hard part is memorizing it, but after a while it becomes routine.

- Algebra Quadratic Equations -
**Reiny**, Friday, February 15, 2008 at 8:16am
I use the following rule:

If the coefficient of the squared term is 1 and the coefficient of the first degree term is even, then I would use completing the square, otherwise just use the quadratic formula

e.g.

x^2 - 12x -5 = 0

x^2 - 12x = 5

x^2 - 12x + 36 = -5 + 36

(x-6)^2 = 31

x = 6 ± √31

In this case this method is actually faster and easier than using the formula, since the formula answer has to be broken down to lowest terms.

- Algebra Quadratic Equations -
**Marysvoice**, Friday, February 15, 2008 at 9:29am
Cool rule, thank you.

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