Which of the following expression is same as the given expression:
$x^{2} + 5 x + 4$

${(x + \frac{5}{2})}^{2} + (\frac{9}{4})$

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${(x - \frac{5}{2})}^{2} + (\frac{9}{4})$

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${(x + \frac{5}{2})}^{2} - (\frac{9}{4})$

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${(x - \frac{5}{2})}^{2} - (\frac{9}{4})$

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Solution

The correct option is C
${(x + \frac{5}{2})}^{2} - (\frac{9}{4})$

${(x + \frac{5}{2})}^{2} - \frac{9}{4} = x^{2} + 5 x + (\frac{25}{4}) - (\frac{9}{4})$
$= x^{2} + 5 x + 4$

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