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

• Algebra Quadratic Equations -

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 -

Thank you.

• Algebra Quadratic Equations -

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 -

Thank you for the example.

• Algebra Quadratic Equations -

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 -

Cool rule, thank you.

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