Question

What value completes the square for the expression
x^2 + 12x

a. −36 c. 6
b. −6 d. 36

Answer 1

Correct Answer: Option D. 36

The given expression is:

$x^{2} +12x$

The formula for a whole square is:

$(a+b)^{2} = a^{2} +2ab+ b^{2}$

Re-writing the given expression we get:

$x^{2} +2(x)(6)$

Comparing this expression with the formula of whole square, we can note that we have the square of first term which x, twice the product of first and second term which are x and 6. What is missing is the square of second term. The second term is 6, and square of 6 is 36. This means addition of 36 to the given expression will make it a complete square.

So, complete square will be:

$x^{2} +2(x)(6)+ 6^{2} =(x+6)^{2}$

So, correct answer is Option d. 36