Completing the Square (Express in the Form \({{\left( x+a \right)}^{2}}+b\))

Completing the Square (Express in the Form \({{\left( x+a \right)}^{2}}+b\))

Secondary 3

Express each of the following expressions in the form \({{\left( x+a \right)}^{2}}+b\) .

  1. \({{x}^{2}}+6x\)
  2. \({{x}^{2}}-3x\)
  3. \({{x}^{2}}+\frac{4}{5}x\)
  4. \({{x}^{2}}-2\frac{1}{2}x\)

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Answer:(i) \({{\left( x+3 \right)}^{2}}-9\) (ii) \({{\left( x-1.5 \right)}^{2}}-2.25\) (iii) \({{\left( x+\frac{2}{5} \right)}^{2}}-\frac{4}{25}\) (iv) \({{\left( x-1.25 \right)}^{2}}-1.5625\)

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