Question

X² - 24x + c
Find the answer for C.

Answer 1

`c=-x^(2) +24x`

Step-by-step explanation:

Subtract on both sides to isolate c.

`x^(2) -24x+c\\x^(2) -24+c-c=-c\\x^(2) -24+0=-c\\x^(2) -24x=-c\\-c=x^(2) -24x`

Have c be in positive form.

`-c=x^(2) -24x\\(-)(-c)=(-)(x^(2) -24x)\\c=-x^(2) +24`

Answer 2

Divide the coefficient of
x
(not
x
2
) by 2, and then square that.
c
=
144
.
Step-by-step explanation:
Divide the coefficient of
x
(not
x
2
) by 2, and then square that.
So for
x
2
−
24
x
, dividing
−
24
by
2
gets us
−
12
.
Squaring
−
12
gets us
144
,
So
c
=
144
.
In general:
Consider the factoring identity

(
x
−
a
)
2
=
x
2
−
2
a
x
+
a
2
If we only have the middle term,
−
2
a
x
, then dividing the middle term by
2
x
gets us

−
2
a
x
2
x
=
−
a
(If we only take the coefficient on
x
, we do not have to divide by
x
.)
Then if we square that, we get

(
−
a
)
2
=
a
2
So as you can see, taking the coefficient on
x
, dividing it by
2
, and then squaring it will get us the magic constant that lets us complete the square.