Question

If using the method of completing the square to solve the quadratic equation x²-13x+31=0, which number would have to be added to "complete the square"?

Answer 1

The number that needs to be added to complete the square is half of the coefficient of x, squared.

Step-by-step explanation:

The quadratic equation x² - 13x + 31 = 0 can be solved by completing the square. To do this, we need to add a number to the equation in order to create a perfect square trinomial. The number that needs to be added is half of the coefficient of x, squared. In this case, the coefficient of x is -13, so we add (-13/2)² to both sides of the equation.

x² - 13x + (-13/2)² + 31 - (-13/2)² = 0

By simplifying and factoring, we obtain (x - (13/2))² = (35/4). From here, we can solve for x by taking the square root of both sides and isolating x.

x - (13/2) = ±√(35/4)

x = (13 ± √35)/2