1. Fred Dillon dillon314@sbcglobal.net
COMPLETING THE SQUARE
Fred Dillon

2. Mindful Manipulation
We can also look at our original problem a different way.
We want to replace x by z = x – m, so that x x – 144, when expressed as a polynomial in z, has no linear term – it looks like z2 + p for some number p.
x2 + 10x – 144 = (x – m)2 + p
Graham, K., Cuoco, A., & Zmmermann, G. (2010). Focus in High School Mathematics: Reasoning and Sense Making in Algebra. Reston, VA:NCTM

3. Mindful Manipulation -2m = 10 (-5)2 + p = -144 m = -5 p = -169
x2 + 10x – 144 = (x – m)2 + p x2 + 10x – 144 = x2 – 2mx + m2 + p
m2 + p = -144 and
(-5)2 + p = -144
p = -169
-2m = 10
m = -5
x2 + 10x – 144 = (x + 5)2 – 169

4. Work Sample