If the expression x2+ x + 1 is written in the form x + 12

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If the expression x²+ x + 1 is written in the form x + 1 ² + q²,
2
then the possible values of q are

x² + x + 1

= x² + 2.x.	1	+	1	+	3
	2		4		4

=		x +	1		²	+		±	√3		²
			2						2

∴		x +	1		²	+		±	√3		²
			2						2

=		x +	1		²	+ q²
			2

⇒ q = ±	√3
	2

If the expression x²+ x + 1 is written in the form		x +	1		²	+ q²,
			2