To complete the square for the quadratic equation x² + 3x + 6, we first focus on the terms involving x. The goal is to transform the expression into a perfect square trinomial.
1. Start with the expression without the constant: x² + 3x.
2. To find the number to complete the square, take the coefficient of x (which is 3), divide it by 2, and then square it:
- 3 ÷ 2 = 1.5
- 1.5² = 2.25
3. This means we need to add 2.25 to both sides of the equation.
4. Now, let’s rewrite the equation:
x² + 3x + 2.25 = 6 + 2.25
5. Simplifying the right side gives you x² + 3x + 2.25 = 8.25.
In summary, the number that should be added to both sides of the equation to complete the square is 2.25.