Question

What number should be added to $x^2+6x$ to make it a perfect square?

• 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.
If we observe carefully we can understand that $x^2+6x$ can be made into the form $(a^2+2ab+b^2)$ by adding a constant. $b^2$ is the constant that needs to be added.
To make $x^2+6x$ a perfect square, divide the co-efficient of $x$ by 2 and the add the square of the result to make it a perfect square.
Hence, $\frac{6}{2}=3$ and $3^2=9.$
So, we should add 9 to make $x^2+6x$ a perfect square.

i.e. $x^2+6x+9=(x+3{)}^2$