Question

If using the method of completing the square to solve the quadratic equation

x² + 20x - 6 = 0, which number would have to be added to "complete the square"?

a) 100
b) 150
c) 225
d) 400

Answer 1

To complete the square for the quadratic equation x² + 20x - 6 = 0, we add the square of half the coefficient of x, which is 100, making the correct answer (a) 100.

Step-by-step explanation:

The question involves solving a quadratic equation by the method of completing the square. In the given equation, x² + 20x - 6 = 0, to complete the square, we first focus on the x² and 20x terms. To transform the x² + 20x into a perfect square trinomial, we need to find a number that, when added, completes the square. We look for the square of half of the coefficient of x, which in this case is 10 (half of 20). Squaring 10 gives us 100, which is the number we must add to both sides of the equation to complete the square.

Therefore, the answer is (a) 100.