Completing the Square and Related Craziness

Try these: Note: the notation ^2 will mean squared as I do not know how to create superscripts in html.

FOIL

1. (x+2)^2
2. (x-3)^2
3. (x-4)^2
4. (x+5)^2
5. (x+3/4)^2
6. (x+k)^2
7. (3x+2)^2
8. (3x-1)^2
9. (4x-4)^2
10. In a perfect square trinomial (the result of squaring a binomial) ______ of the coeffiecient middle term is always equal to the square root of the last term.
11. Another way of saying that is the _______ of ____ of the middle term is ______ to the last term.

Analyze:

Determine if the following are perfect square polynomials. If they are write them as the square of a binomial. If not show me why and write "not a perfect square".Here's an example of what I'm looking for:

Example: x^2 + 12x + 36

Possible Answers:

"Yes, because 12 divided by two is 6 and 6^2 = 36. The last term is the square of half the coefficient of the middle term."

or

"Yes, because the square root of 36 doubled is 12"

1. x^2 + 5x + 10
2. x^2 + 3x + 9
3. x^2 + 6x + 12
4. x^2 - 2x + 1
5. x^2 - 5x + 25
6. x^2 -3x + 9/4
7. x^2 - 8x + 16

Evaluate:

Find the value of c for which ax^2 + bx + c is a perfect square trinomial

Hint: c must always equal (b/2)^2 for ax^2 + bx + c to factor into (x + b/2)^2

1. x^2+ 6x + c
2. x^2 + 14x + c
3. x^2 - 8x + c
4. x^2 - 16x + c
5. x^2 + 5x + c
6. x^2 -2/5x + c

Solve:

Finally use the method of completing the square to solve the following problems

Example: 2x^2 -3x = 5

Explanation:

Divide everything by 2 to get x^2 -3/2x = 5/2
then divide -3/2 by 2 (that is -3/4) and add the square of -3/4 to both sides.
That is, add 9/16 to both sides.
Your result is x^2 -3/2x + 9/16 = 5/2 + 9 /16.
Now the left side can be factored to the square of a binomial and the right can be simplified into 41/16.
So x^2 - 3/2x + 9/16 becomes (x - 3/4)^2 = 41/16
This result can be solved by employing the squareroot property in the same fashion as you did for the ones above.

1. x^2 + 6x = 5
2. x^2 - 16x = -70
3. x^2 +18x = -6
4. y^2 + 20y = -40
5. m^2 + 18m + 100 = 0
6. 2x^2 - 16x = 6
7. 5t^2 - 60t = -20
8. 2x^2 +16x -8 = 0
9. m^2 + 8m -9 = -5

Hint: On the 6 - 8, you will need to divide by the
coeffecient of the x^2 term before doing anything else.