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 see that $x^2+6x$ can be written in the form $(a^2+2ab+b^2)$ by adding a constant.
$x^2+2\left(x\right)\left(3\right)+constant$.
To make $x^2+6x$ a perfect square, divide the coefficient of x by 2 and add the square of the result to make this a perfect square.
Hence $\frac{6}{2}=3$ and $3^2=9.$
We should add 9 to make $x^2+6x$ a perfect square.