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:

`(-(15)/(2))^2=(225)/(4)`
`\begin{gathered} x^2-15x+(225)/(4)=10+(225)/(4) \\ \\ x^2-15x+(225)/(4)=(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