Question

If using the method of completing the square to solve the quadratic equation x^2 - 15x - 10 = 0, which number would have to be added to "complete the square"?

Answer 1

$x^2-15x-10=0$

Completing the square method:

$ax^2+bx+c=0$

1. Move the constants to one side. Move the constant term c to the right side of the equation:

$x^2-15x=10$

2. Add (b/2)^2 to both sides:

Find (b/2)^2:

$(-\frac{15}{2})^2=\frac{225}{4}$$\begin{gathered} x^2-15x+\frac{225}{4}=10+\frac{225}{4} \\ \\ x^2-15x+\frac{225}{4}=\frac{265}{4} \\ \end{gathered}$The number you need to add in both sides of the equation to complete the square is 225/4

3. Factor and solve