To complete the square for the equation \( x^2 + 3x = 6 \), we need to find the number that we should add to both sides of the equation.
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Start with the expression on the left side: \( x^2 + 3x \).
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Take the coefficient of \( x \) (which is 3), divide it by 2, and square it: \[ \left(\frac{3}{2}\right)^2 = \frac{9}{4} \]
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Now, you should add \( \frac{9}{4} \) to both sides of the equation.
Thus, the number that should be added to both sides of the equation to complete the square is \( \frac{9}{4} \).
If we write it out: \[ x^2 + 3x + \frac{9}{4} = 6 + \frac{9}{4} \]
So, the answer is \( \frac{9}{4} \).
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