Question

if using the method of completing the square to solve the quadratic equation x squared + 16x - 5 equals 0 which number would have to be added to complete the square

Answer 1

Given the quadratic equation :

`x^2+16x-5`

It is required to make a complete square

The coefficient of x = 16

so, we will add : the square of ( half of the coefficient x )

so, half of 16 = 0.5 * 16 = 8

Square of 8 = 64

So, the complete square will be as following ;

`\begin{gathered} x^2+16x-5+64-64 \\ =x^2+16x+64-5-64 \\ =(x^2+16x+64)+(-5-64) \\ =(x+8)^2+(-69) \\ \\ =(x+8)^2-69 \end{gathered}`