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

Mindful Manipulation We can also look at our original problem a different way. We want to replace x by z = x – m, so that x2 + 10x – 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

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

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