Processing Math: Done

From Förberedande kurs i matematik 1

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	As always when completing the square, we focus on the quadratic and linear terms		As always when completing the square, we focus on the quadratic and linear terms
-	<math>2x-x^{2}</math>	+	<math>2x-x^{2}</math>, which we also can write as
-	, which we also can write as	+
	<math>-\left( x^{2}-2x \right)</math>		<math>-\left( x^{2}-2x \right)</math>
	. If we neglect the minus sign, we can complete square of the expression		. If we neglect the minus sign, we can complete square of the expression

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Revision as of 11:20, 12 September 2008

As always when completing the square, we focus on the quadratic and linear terms 2x−x2, which we also can write as −x2−2x  . If we neglect the minus sign, we can complete square of the expression 2x−x2 by using the formula

x2−ax=x−2a2−2a2 

and we obtain

x2−2x=x−222−222=x−12−1 

This means that

5+2x−x2=5−x2−2x=5−x−12−1=5−x−12+1=6−x−12

A quick check shows that we have completed the square correctly.:

6−x−12=6−x2−2x+1=6−x2+2x−1=5+2x−x2