What is the first step to solve the equation 3x² + 18x + 21 by completing the square?

To solve the equation 3x² + 18x + 21 = 0 by completing the square, the first step involves simplifying the equation. Here’s how to start:

1. Factor out the coefficient of x²: Since the coefficient of x² is 3, we want to factor it out from the first two terms:

3(x² + 6x) + 21 = 0

Now our equation looks like this:

3(x² + 6x) + 21 = 0

2. Isolate the constant term: Move the constant term (21) to the other side of the equation:

3(x² + 6x) = -21

3. Divide by the coefficient of x²: To prepare for completing the square, divide both sides by 3:

x² + 6x = -7

At this point, we have prepared our equation to complete the square. The first step is, therefore, to factor out the 3 from the first two terms and isolate the terms involving x. From here, you can proceed to complete the square by adding and subtracting the square of half the coefficient of x (which is 3 in this case) on the left side to maintain the equality.