Final answer:
To complete the square for the equation x² + 5x - 37 = 0, we take half of the coefficient of x (which is 5/2 or 2.5), and square it, resulting in 6.25. Therefore, 6.25 would need to be added to complete the square, but this is not an option provided in the question.
Step-by-step explanation:
To solve the quadratic equation x² + 5x - 37 = 0 by the method of completing the square, you need to add a certain number that transforms the equation into a perfect square trinomial.
The general formula for a perfect square trinomial is (x + a)² = x² + 2ax + a². To find the value of a, we look at the coefficient of x, which is 5 in our equation. We then take half of 5, which is 2.5, and square it, resulting in 6.25. Therefore, we would need to add 6.25 to both sides of the equation to complete the square. However, since this number is not one of the options provided, we must clarify the question.
It seems that there is a discrepancy between the options provided and the answer obtained. In order to have one of the numbers provided as an option, the coefficient of x would have to be an even number. Hence, without altering the coefficient, the number to add to complete the square would not match any of the choices given - it would be 6.25.