To complete the square for the equation \(x^2 + 7x = 4\), we want to transform the left side into the form \((x + a)^2\).
The general formula to complete the square for a quadratic equation \(x^2 + bx\) is to add \(\left(\frac{b}{2}\right)^2\). Here, \(b = 7\).
- Calculate \(\frac{b}{2} = \frac{7}{2}\).
- Now square this value: \(\left(\frac{7}{2}\right)^2 = \frac{49}{4}\).
So, to complete the square, we add \(\frac{49}{4}\) to both sides of the equation \(x^2 + 7x = 4\).
The options provided seem to be a bit different. The correct value you add to both sides to complete the square is:
\[ \left(\frac{7}{2}\right)^2 \]
Therefore, the answer is \(\left(\frac{7}{2}\right)^2\).
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