Question

If using the method of completing the square to solve the quadratic equation x² - 19x - 3 = 0, which number would have to be added to "complete the square"?

1) 9.5
2) 9.25
3) 9
4) 8.75

Answer 1

To complete the square for the equation x² - 19x - 3 = 0, we would add (9.5)², which equals 90.25. However, based on the options provided, the closest match is 9.25, indicating a possible typo since it should have been 90.25.

Step-by-step explanation:

To complete the square for the quadratic equation x² - 19x - 3 = 0, we focus on the x-terms. The general form of a quadratic equation that has been completed is x² + bx + (b/2)², which creates a perfect square trinomial. In the given equation, the coefficient b of the x term is -19. To complete the square, we need to add (-19/2)², or (-9.5)², to the equation. This yields (9.5)², which is 90.25. Thus, the number we need to add to complete the square is 90.25.

However, the correct value was expected from given options, and the number closest to our result is 9.25 (option 2), which is likely a typo in the question because the options provided seem to be missing a digit. The actual calculation without the typo should be (-19/2)² = 90.25