Complete the square: x^2 -12x. Which of the following is the correct perfect-square trinomial?
the answers are:
a.) x^2 +22x+121
b.) x^2 -10x+25
c.) x^2 -20x+44
d.) x^2 -12x+36
This is tough because the answers could be a.) b.) and d.)
I am not sure which to choose.
You are seeing something the rest of us isn't. Only one answer has -12x in it.
To complete the square, you divide the number before the x by 2, square it, and add it to the end. The answer is d.
To complete the square for the given expression x^2 - 12x, follow these steps:
1. Take half of the coefficient of the x term, which is -12, and square it: (-12/2)^2 = (-6)^2 = 36.
2. Add the result from step 1 to both sides of the expression:
x^2 - 12x + 36 = 36.
Now, let's look at the answer choices:
a.) x^2 + 22x + 121: This does not match the result we obtained.
b.) x^2 - 10x + 25: This also does not match the result we obtained.
c.) x^2 - 20x + 44: This does not match the result we obtained.
d.) x^2 - 12x + 36: This matches the result we obtained by completing the square.
Therefore, the correct perfect-square trinomial is option d.) x^2 - 12x + 36.