Solution 2.3:1a

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Current revision (13:22, 26 September 2008) (edit) (undo)
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If we consider the squaring rule
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If we consider the rule
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{{Displayed math||<math>(x-a)^{2} = x^{2}-2ax+a^{2}</math>}}
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<math>\left( x-a \right)^{2}=x^{2}-2ax+a^{2}</math>
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and move <math>a^{2}</math> over to the left-hand side, we obtain the formula
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and move
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{{Displayed math||<math>(x-a)^{2}-a^{2} = x^{2}-2ax\,\textrm{.}</math>}}
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<math>a^{2}</math>
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over to the left-hand side, we obtain the formula
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With the help of this formula, we can rewrite (complete the square of) a mixed expression <math>x^{2}-2ax</math> to a obtain a quadratic expression, <math>(x-a)^{2}-a^{2}</math>.
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<math>\left( x-a \right)^{2}-a^{2}=x^{2}-2ax</math>
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The expression <math>x^{2}-2x</math> corresponds to <math>a=1</math> in the formula above and thus
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{{Displayed math||<math>x^{2}-2x = (x-1)^{2}-1\,\textrm{.}</math>}}
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<math></math>
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With the help of this formula, we can rewrite (complete the square of) a mixed expression
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<math>x^{2}-2ax</math>
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to a obtain a quadratic expression,
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<math>\left( x-a \right)^{2}-a^{2}</math>
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The expression
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<math>x^{2}-2x</math>
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corresponds to
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<math>a=1</math>
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in the formula above and thus
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<math>x^{2}-2x=\left( x-1 \right)^{2}-1</math>
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Current revision

If we consider the rule

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

and move \displaystyle a^{2} over to the left-hand side, we obtain the formula

\displaystyle (x-a)^{2}-a^{2} = x^{2}-2ax\,\textrm{.}

With the help of this formula, we can rewrite (complete the square of) a mixed expression \displaystyle x^{2}-2ax to a obtain a quadratic expression, \displaystyle (x-a)^{2}-a^{2}.

The expression \displaystyle x^{2}-2x corresponds to \displaystyle a=1 in the formula above and thus

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