Question

Complete the square to form a perfect square trinomial
x^2-12x+

Answer 1

a perfect square is composed by:
\[(a+b)^2= a^2 +ab + b^2\]
in other words:
"the first term squared, plus, two times the first times the second plus the second squared"

Answer 2

I don't understand

Answer 3

I don't understand

Answer 4

All you have to do, is check the variables and see what you need to complete it.
Since the structure was:
\[(ax+b)^2=ax^2+2axb+b^2\]
And you have:
\[x^2-12x+...\]
We can easily see that a=1, so we need a number, that makes 2ab=-12
So that be, since a=1:
b=12/2
b=-6
So, now we have, in order to complete the perfect square, make the b^2, but since we deduced it was -6, we only square it:
-6^2=36
so therefore:
\[x^2-12x+36=(x-6)^2\]

Answer 5

Your function resembles the quadratic \(ax^2+bx+c\).

You're looking for a C value to complete your quadratic function. To find it, use the formula: \[c=\left(\frac{b}{2}\right)^2\] In this case, \[c=\left(\color{red}{\frac{-12}{2}}\right)^2 =(\color{red}{-6})^2= 36\]To complete your quadratic, just plug in your c value. \[x^2-12x+36 \implies \left(x+\color{red}{\frac{b}{2}}\right)^2\implies (x\color{red}{-6})^2\]