math help please!!!!!

Question

If using the method of completing the square to solve the quadratic equation x2+7x+30=0, which number would have to be added to "complete the square"?

Answer 1

When completing the square, you first need to separate the "x²" and "x" terms from the constant:

x² + 7x +30 = 0 original equation

(x² + 7x) + 30 = 0 separating the "x²" and "x" terms from the constant

Now that we have them separated, we are going to deal with completing the square of what is in the parenthesis, (x² + 7x). What you do is take the 7 and divide it by 2 to get 3.5. The square is now going to be

(x + 3.5)². When you work this out (FOIL) you get x² + 7x + 12.25. In order to preserve the original equation, you must subtract 12.25. In other words, this is what it would look like:

(x² +7x + 12.25) + 30 - 12.25 = 0

(x + 3.5)² + 17.75

So, I guess the answer that is being asked for would be 12.25.

Hope this helps!