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

We know that $(a+b{)}^2=(a^2+2ab+b^2)$, where $(a+b{)}^2$ 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 to it.

On comparing $(x^2+2(x\left)\right(3)+constant)$ with $a^2+2ab+b^2$ we can say that $3^2=9$ should be added.

Now, $x^2+2\left(x\right)\left(3\right)+9=(x+3{)}^2$

where $(x+3{)}^2$ is a perfect square.

So, 9 should be added to $x^2+6x$ to make it a perfect square.