From Förberedande kurs i matematik 1

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-	{{NAVCONTENT_START}}	+	When we complete the square, it is only the first two terms, <math>x^{2}+2x</math>, that are involved. The general formula for completing the square states that <math>x^{2}+ax</math> equals
-	<center> [[Image:2_3_1b.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\Bigl(x+\frac{a}{2}\Bigr)^{2} - \Bigl(\frac{a}{2}\Bigr)^{2}\,\textrm{.}</math>}}
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		+	Note how the coefficient ''a'' in front of the ''x'' turns up halved in two places.
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		+	If we use this formula, we obtain
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		+	{{Displayed math||<math>x^{2}+2x = \Bigl(x+\frac{2}{2}\Bigr)^{2} - \Bigl(\frac{2}{2}\Bigr)^{2} = (x+1)^{2}-1</math>}}
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		+	and if we subtract the last "1", we obtain
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		+	{{Displayed math||<math>x^{2}+2x-1 = (x+1)^{2}-1-1 = (x+1)^{2}-2\,\textrm{.}</math>}}
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		+	To be completely certain that we have used the correct formula, we can expand the quadratic on the right-hand side,
		+
		+	{{Displayed math||<math>(x+1)^{2}-2 = x^{2}+2x+1-2 = x^{2}+2x-1</math>}}
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		+	and see that the relation really holds.

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Current revision

When we complete the square, it is only the first two terms, \displaystyle x^{2}+2x, that are involved. The general formula for completing the square states that \displaystyle x^{2}+ax equals

\displaystyle \Bigl(x+\frac{a}{2}\Bigr)^{2} - \Bigl(\frac{a}{2}\Bigr)^{2}\,\textrm{.}

Note how the coefficient a in front of the x turns up halved in two places.

If we use this formula, we obtain

\displaystyle x^{2}+2x = \Bigl(x+\frac{2}{2}\Bigr)^{2} - \Bigl(\frac{2}{2}\Bigr)^{2} = (x+1)^{2}-1

and if we subtract the last "1", we obtain

\displaystyle x^{2}+2x-1 = (x+1)^{2}-1-1 = (x+1)^{2}-2\,\textrm{.}

To be completely certain that we have used the correct formula, we can expand the quadratic on the right-hand side,

\displaystyle (x+1)^{2}-2 = x^{2}+2x+1-2 = x^{2}+2x-1

and see that the relation really holds.