Answer:
36 should be added to make the left side a perfect square.
Step-by-step explanation:
We know that [tex]a^{2} +2ab+b^{2} =(a+b)^{2}[/tex]
If we compare the first two terms of the left side with [tex]x^{2} +12x[/tex], we get,
a = x,
2ab = 12x
But since a = x,
2xb = 12x
Cancel x both sides and divide both sides by 2.
b = 6
So, [tex]b^{2} =6^{2} =36[/tex] should be added to the left side to make it a perfect square.
[tex]x^{2} +12x+36=40+36[/tex]
[tex](x+6)^{2} =76[/tex]
