Question

The number that is to be added to $x^2+6x$ to make the resultant a perfect square is .

• A. 36
• B. 18
• C. 9
• D. 72

Answer 1

The correct option is C 9

The identity $(a+b{)}^2=a^2+2ab+b^2$ represents a perfect square.
Consider the expression $x^2+6x.$ If we halve the coefficient of $x$ and add its square to this expression, we get
$x^2+6x+9.$
But, $x^2+6x+9=x^2+2\left(x\right)\left(3\right)+3^2$
$=(x+3{)}^2,$ a perfect square.
Thus, we have to add 9 to the expression $x^2+6x$ so that the resultant is a perfect square.