Solving for x by completing the square

Sorry I didn't get a chance to blog last night so this is for yesterdays class, March 12, 2007.

For the first part of class, we looked over our previous test (Trigonometry) and checked for the correct answers amongst our peers. Then we went over how to solve for "x" by completing the square, rather than factoring.

Here are some examples:
1. x² - 4x +2 =0
Like in the Quad Functions unit, we follow the same concept when completing the square. You first focus on the "x² - 4x" and try to find the third term by taking the "4x" divide it by "2" and then square it. Then balance the equation by subtracting the "4" on the outside of the brackets.
( x² - 4x + 4 ) + 2 - 4 = 0
Now you can find the perfect square (x-2)² and put together the like terms ( 2 and -4)
( x - 2 )² -2 = 0
Basically all that's left to do, is to simply isolate "x"
( x - 2 )² = 2
x - 2 = ( + or - ) (the square root of) 2
x = 2 (+ or - ) (the square root of) 2
* sorry i don't know how to make the square root sign.

In this case, as in most, there are 2 roots:
x = 2 + ( the square root of ) 2 ( here, the square root of 2 is positive)
or
x = 2 - ( the square root of ) 2 ( here, the square root of 2 is negative)

2. This example follows the same concept as the first.
x² + 8x - 45 = -36
x² + 8x - 9 = 0
( x² + 8x + 16 ) - 9 - 16 = 0
( x + 4 )² - 25 = 0
(x + 4)² = 25
x + 4 = ( + or - ) (the square root of) 25
x = ( + or - ) (the square root of) 25 - 4

The 2 roots are:
x = 5 - 4 = 1 ( here the square root of 25 was positive, therefore it equals +5)
or
x = -5 -4 = 9 ( here the square root of 25 is negative, therefore it equals -5)

So this is basically what we did yesterday, and the blog for today is Shelly.