Question

If using the method of completing the square to solve the quadratic equation x, squared, plus, 7, x, plus, 30, equals, 0x 2 7x 30=0, which number would have to be added to "complete the square"?

Answer 1

To complete the square for x^2 + 7x + 30 = 0, you need to add (7/2)^2, which is 12.25, to form a perfect square trinomial.

Step-by-step explanation:

To complete the square for the quadratic equation x2 + 7x + 30 = 0, you first need to find a number that makes the expression x2 + 7x into a perfect square trinomial. A perfect square trinomial has the form (x + a)2 = x2 + 2ax + a2, where a is the number we need to find. In this case, you would take half of the coefficient of x, which is 7/2, and then square it, resulting in (7/2)2 or 12.25. Therefore, you have to add 12.25 to both sides of the equation to complete the square.