Question

If using the method of completing the square to solve the quadratic equation x^2 - 10x + 21 = 0, which number would have to be added to "complete the square"?

a. 5
b. 10
c. 15
d. 20

Answer 1

To complete the square in the equation x^2 - 10x + 21 = 0, one would have to add 25, resulting in (x - 5)^2 - 4 = 0.

Step-by-step explanation:

To answer which number would have to be added to complete the square in the quadratic equation x^2 - 10x + 21 = 0, we need to follow a few steps characteristic of the completing the square method. First, we find the coefficient of the x term (which is -10), divide it by 2, and then square the result. So, (-10 / 2)^2 equals 25. Therefore, the number we need to add to complete the square is 25. However, we must also subtract 25 to maintain the equation's balance, and thus, the new form of the equation would be x^2 - 10x + 25 - 4 = 0, which simplifies to (x - 5)^2 - 4 = 0.