Question

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

Answer 1

Answer:

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

Step-by-step 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 $(\frac{b}{2a})^2$

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

This implies that:

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

The expression in the rectangle is a perfect square

$(x+6)^2-41$

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