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Liula [17]
2 years ago
8

X^2-x-2=0 as a complete square

Mathematics
1 answer:
laila [671]2 years ago
3 0

Answer:

x_1=2; x_2=-1

Step-by-step explanation:

The square term is x^2 so we expect the complete square to be of the form (x-a) ^2=x^2+2ax+a^2.

Let's compare the first degree terms now: we have 2ax on one side and -1x on the other. That would make a=- \frac12. At this point we have still the second squared term, so we add and subtract \frac14 = (\frac12)^2

Our equation becomes:

x^2-x+\frac14 -\frac14-2 =0\\(x-\frac12)^2-\frac94=0

(the \frac94 term comes from rewriting 2= \frac84 and adding the terms out of the bracket).

At this point it's just solving the equation:

(x-\frac12)^2 = \frac94 \rightarrow x-\frac12=\pm\frac32\\x=\frac12\pm\frac32\\x_1=\frac42 = 2; x_2=\fra-\frac22=-1

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