Answer:
[tex]x^2+12x-5=(x+6)^2-41[/tex]
Step-by-step explanation:
The given expression is [tex]x^2+12x-5[/tex]
Comparing to [tex]ax^2+bx+c[/tex], we have [tex]a=1,b=12,c=-5[/tex]
We add and subtract [tex](\frac{b}{2a})^2[/tex]
[tex]x^2+12x+6^2-6^2-5[/tex]
This implies that:
[tex]\boxed{x^2+6x+36}-36-5[/tex]
The expression in the rectangle is a perfect square
[tex](x+6)^2-41[/tex]
Therefore [tex]x^2+12x-5=(x+6)^2-41[/tex]
