Goal: Transform x^2 + a*x + b to (x + c)^2 + d.
Setting the two sides equal to each other:
x^2 + a*x + b = (x + c)^2 + d
x^2 + a*x + b = x^2 + 2*c*x + c^2 + d
Next I will use a technique that calculus students normally use when decomposing partial fractions.
Setting the coefficients of x^2, x, and the constant equal to each other, we have:
x^2: 1 = 1
x: a = 2*c
constant: b = c^2 + d
Solving for c:
a = 2*c
c = a/2
Then solving for d:
b = c^2 + d
b = a^2/4 + d
d = b  a^2/4
Hence:
x^2 + a*x + b = (x + a/2)^2 + (b  a^2/4)
Hope this helps. Until next time!
Eddie
This blog is property of Edward Shore. 2013
A blog is that is all about mathematics and calculators, two of my passions in life.
Monday, August 12, 2013
Completing the Square
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