Question

complete the square.

x^2 - 6x + ____

show all work

Answer 1

1/2 of 6 is?

Answer 2

So we want to start solving it like this: x^2 -6x + ______ = 0 + ______

In completing the square,we're trying to put the given formula in the format ax^2 + bx +c and in order to do that we need to find our C first.

In finding our C, we can use what is given, b. To find C we use the formula \[\large c=(\frac{b}{2})^2\]
our b in this case is -6\[\large c =(\frac{-6}{2})^2= (-3)^2 =9\]Now we add 9 to BOTH sides of the equation. \[\large x^2 - 6x +9 = 0+9\] simplifying this, we will have put it in the format \[\large (x+b)^2 = c\] so rewriting x^2 -6x + 9 = 9 we will have \[\large (x-3)^2 = 9 \] Now to write it in proper form,we will move the 9 to the other side. \[\large (x-3)^2-9=0\]

Answer 3

very good, i am still confused as to what number to fill in on the square though.

Answer 4

refer to steps 2 and 3

Answer 5

got it thanks

Answer 6

By that i meant

\[\large c =(\frac{-6}{2})^2= (-3)^2 =9\] because C is our "missing (blank spaced)" value,and we're using the value of our given, b, to solve for it. So the blank space you're trying to fill in will be found by evaluating our function his way. \[\large x^2 - 6x +9 = 0+9\] this is where you fill in those values found, the "9" you found from evaluating b