COMPLETING THE SQUARE (PENYEMPURNAAN KUASA DUA)
II. How to Do It
Of course, you won’t get it so simple in tests… in Section I you could do x2 + 6x + 8 because I already told you that x2 + 6x + 9 = (x + 3)2. Now look at this:
x2 - 5x + 27
Jeng jeng jeng! You have no idea what to turn 27 into, right? Don’t worry, there’s a systematic way to do it. Look at it as ax2 + bx + c.
This is because [(5/2)2 - (5/2)2] equals nothing. So even though it LOOKS like you added something to the equation, you actually didn’t (you buruk siku: give people something and take it away again).
To recap,
f(x) = x2 – 5x + 27
= x2 - 5x + &nnbsp; + 27
= x2 - 5x + (5/2)2 - (5/2)2 + 27 <~(see i)
= (x - 5/2) 2 - (5/2)2 + 27
= (x - 5/2) 2 + 83/4 <~(see ii)
i) b is 5, so you put (5 4 2) in the brackets.
ii)
- (5/2)2
+ 27 = - 25/4 + 108/4
= 83/4
The red part is just to show you what’s going on. Your teacher won’t be happy if you wrote the red part in your paper.
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