Question

What number should be added to both sides of the equation to complete the square?

x2 + 3x = 6


(StartFraction 3 Over 2 EndFraction) squared
3
62

Answer 1

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.

1. Start with the expression on the left side: \( x^2 + 3x \).
2. Take the coefficient of \( x \) (which is 3), divide it by 2, and square it:
\[
\left(\frac{3}{2}\right)^2 = \frac{9}{4}
\]

3. 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 \( \frac{9}{4} \).