Essentially, we are trying to find the missing constant term of [tex](x - a)^2[/tex] (remember that we are subtracting [tex]a[/tex] due to the negative sign in front of the second term). Let's expand this to see what we can work with:
[tex](x - a)^2[/tex]
[tex]x^2 - ax - ax + a^2 = x^2 - 2ax + a^2[/tex]
Now, we know the second term is [tex]12x[/tex], so let's set the second term in the polynomial we just found equal to [tex]12x[/tex]:
[tex]2ax = 12x[/tex]
[tex]2a = 12[/tex]
- Divide both sides of the equation by [tex]x[/tex]
[tex]a = 6[/tex]
- Divide both sides of the equation by 2
We have found [tex]a = 6[/tex]. We know the missing constant term is [tex]a^2[/tex], according to the polynomial we found earlier. Thus, the missing term is:
[tex]a^2 \Rightarrow 6^2 = 36[/tex]
The missing constant term is 36.
