Question

Complete the square for x^2+12x-5.

Answer 1

`x^2+12x-5=(x+6)^2-41`

Explanation:

The given expression is
`x^2+12x-5`

Comparing to
`ax^2+bx+c`, we have
`a=1,b=12,c=-5`

We add and subtract
`((b)/(2a))^2`

`x^2+12x+6^2-6^2-5`

This implies that:

`\boxed{x^2+6x+36}-36-5`

The expression in the rectangle is a perfect square

`(x+6)^2-41`

Therefore
`x^2+12x-5=(x+6)^2-41`