Question

What number should be added to $x^2+12x$ so that the resultant is a perfect square?

• A. 72
• B. 36
• C. 18
• D. 144

Answer 1

The correct option is B 36

The identity $(a+b{)}^2=a^2+2ab+b^2$ represents a perfect square.
Consider the expression $x^2+12x.$ If we halve the coefficient of $x$ and add its square to this expression, we get
$x^2+12x+36.$
But, $x^2+12x+36=x^2+2\left(x\right)\left(6\right)+6^2$
$=(x+6{)}^2,\text{a perfect square.}$
Thus, we have to add 36 to the expression $x^2+12x$ so that the resultant is a perfect square.