Day 115 Notes Completing the Square with Algebra Tiles
Name:
~~~~~~~~~~~~~-
Period:
Date: - - - -
For each expression,
•
•
•
Find the appropriate algebra tiles.
Try to make them a square.
Take <as many ls tiles as are needed to complete the square.
Expression
x +2x + 'ff
2
Number of 1-tiles needed to
complete the square
Expression written as a square
(side length) 2
f
{
x 2 +4x+ __!i___
'-(
( )(+1.-) 'L
~
I&
( x+nl..
x 2 +6x +
:J...
x 2 +8x+
Ho
()(+<)l.
( X.
~s
x 2 +lOx+ ;/5
~
+'1\1.
{x.f5
,1"
Figure out the following without algebra tiles:
Number of 1-tiles needed to
complete the square
Expression
x 2 +200x+
10
Expression written as a square
(side length) 2
(x-1-
IODO
100
x2 - 4x+
Describe in words how you can find the number of missing 1-tiles:
f O.l<e ho\ ~
~ '· b '· Q"d 4-neA r q,u ru-1
We call this missing number the "magic c"
Write a formula to find c (remember the number in front of the xis b):
c~ (!)~
When you complete the square the expression ALWAYS becomes:
(). rer.fecf s,_uorf
1it.\l"0 ~ l &.
Ltt
•,
Is this trinomial a perfect square trinomial?
2
x + 8x -
l5 = 0
_..45 -15
It sure would be nice if it was . Let's make it a perfect square trinomial.
1.
2. Find the number that would make the left side a perfect square trinomial.
Perfect
c=
(i)
2
•
3. Add that number to both sides of the equation .
4. You now have a perfect square trinomial on the left. How are we sure? We made it
ourselves! Factor it using the shortcut you learned on the front. Write it as a binomial
squared.
X 2 + &°'X+ l(o=
:2.. I
~ ( X -P-1 )d-- ~cl \
5.
(J)~~
c• CCI'{
-u
z.. : 9
Let I s do some \mor
\ el' "" \
'
z + 6x -1
=0
x+
:+rio
~
q : . I +.3_
- ; ~=}TO
1.
X
-3
3+
X -::- 2 _
ID
2x - 5 = 0
3. X
?-~ \
do- L- u
t.?tl~
(
5+_
::.
~J..-
-
( ~ -1):;l
-=J:
x- ,_
--
( - -l-J(o
::t±Jt:
5. xz - 2x - 24
=0
6.
X2
+ 12x =
-3