Re: Simple Stuff...

From: Stan Brown (the_stan_brown_at_fastmail.fm)
Date: 10/06/04 

Date: Wed, 6 Oct 2004 06:58:24 -0400

"jayWHY" <jaywhy@gmail.com> wrote in sci.math:
>Solve for "z" by completing the square.
>z^2 - z = 3/4
>
>Staring long enough, at the above equation, I figured out the answers:
>-1/2 and 3/2. Now how you figure out those answers algebraically by
>completing the square or by any means is where I'm stuck. I can
>factor out a z, but I end having z on both sides of the equation.

Surely your textbook has an example of completing the square. Look
at it again, and follow the pattern. This is good advice for any
homework problem. It is a mystery to me why so many students stare
at homework problems in frustration but will not turn back a few
pages to see what their textbook says about solving them.

Your book probably says something like
    1. Get the constant alone on one side of the equation.
    2. Divide both sides by the coefficient of the squared term, if
it's not 1.
    3. Compute half the coefficient of the first power term, square
that, and add it to both sides.
    4. Rewrite the perfect square trinomial as a squared binomial.
    5. Take positive and negative square roots and solve.

For your example:

1. already done
2. already done
3. (-1/2)^2 = 1/4. Adding to both sides:
        z^2 - z + 1/4 = 3/4 + 1/4
        z^2 - z + 1/4 = 1
4. (z - 1/2)^2 = 1
5. z - 1/2 = 1 or z - 1/2 = -1
    z = 1+1/2 = 3/2 or z = -1 + 1/2 = -1/2 

-- 
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
                                        http://OakRoadSystems.com
Fortunately, I live in the United States of America, where we are
gradually coming to understand that nothing we do is ever our
fault, especially if it is really stupid.            --Dave Barry

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