Question

Math

Answer 1

@Hero

Answer 2

@563blackghost

Answer 3

@Angle

Answer 4

so here we should try to do something called: "Completing the square"

Answer 5

I'll give an example

say, we want to complete the square for f(x) = x^2 + 4x + 5

we try to think of a similar/easier version of that equation
like, say, (x+2)^2 = (x+2)(x+2) = x^2 + 4x + 4
> see how the only difference is the last number?

Answer 6

there is a difference?

Answer 7

\(x^2 + 4x + 5\)
versus
\(x^2 + 4x + 4\)

Answer 8

oh

Answer 9

so while we can say that \(x^2 + 4x + 4 = (x+2)(x+2)\)
it doesn't really work the same for \(x^2 + 4x + 5\)

Answer 10

can you do an example that is similar to my question because im not following

Answer 11

ok, so the main point I was trying to say is that
\(x^2 + 4x + 5 = x^2 + 4x + (4 + 1) = (x^2 + 4x + 4) + 1 = (x+2)(x+2) + 1\)

Answer 12

._.

Answer 13

can you do my question but i do the work

Answer 14

hmm sure, sorry for the confusion x'D I was trying a different approach

so for your question:
first try solving: (x+6)^2 = ?

Answer 15

2x+36

Answer 16

\((x + 6)^2 = (x+6)(x+6) = ?\)

Answer 17

36x?

Answer 18

WAIT its (x+6)^2

Answer 19

right?

Answer 20

can you try expanding it?

Answer 21

(x+6)(x+6)

Answer 22

good
and you can expand it further

Answer 23

x^2+12x

Answer 24

/*

Answer 25

close! I think it's missing something

Answer 26

+26

Answer 27

?

Answer 28

(x+6)(x+6) = (x)*(x) + (x)*(6) + (6)*(x) + (6)*(6)

you got = x^2 + 12x + _(6*6)_ ?

Answer 29

.-.

Answer 30

OH

Answer 31

yeah
6 times 6 = 36
not 26

Answer 32

+36

Answer 33

wonderful!

so
(x+6)^2 = x^2 + 12x + 36

now, how is this different from your question?

Answer 34

+36 ~= +26

Answer 35

^not equal sign fail

Answer 36

exactly!

you see it, that's great :)

so
the idea is that we can add and subtract numbers at the same time and not change anything

like
13 + 10 - 10 is still 13

with this idea
\(x^2 + 12x + 26 + 10 - 10\) still equals the original question right?

Answer 37

Yes

Answer 38

then we can add parts of it but not others like this:

\((x^2 + 12x + 36) - 10\)
I added the 26 + 10 parts together, see?

Answer 39

yuh

Answer 40

then we said before that
(x+6)^2 = x^2 + 12x + 36 right?

Answer 41

yes

Answer 42

so we can say

\(x^2 + 12x + 26\)
\(= (x+6)^2 -10 \)

Answer 43

Thats what my calculator said, but i wanted the steps for future reference, Thanks