What is the first step to solve the equation 2x² + 12x + 32 by completing the square?

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To solve the equation 2x² + 12x + 32 by completing the square, the first step is to simplify the equation by dividing all terms by the leading coefficient (which is 2 in this case). This allows us to work with a simpler quadratic equation.

Here’s how to do it:

  1. Start with the original equation: 2x² + 12x + 32 = 0.
  2. Divide every term by 2:
    x² + 6x + 16 = 0.

Now, our equation is in a more manageable form. The next steps will involve completing the square, but starting by simplifying makes the process easier to follow! After this step, we can focus on manipulating the equation into a perfect square trinomial.

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