Question

Using the completing the square method find the solutions of g(x)?
G(x)=x^2-8x+12
please help me i dont get this at all

Answer 1

x^2 - 8x + 12 = 0

x^2 -8x = -12

take half of 8 and square it, 4^2 =16 .... add to both sides

x^2 -8x + 16 = -12 + 16

(x-4)^2 = 4

x - 4 = +-2

x = 2,6

Answer 2

@dumbcow thank you so much i really appreciate it

Answer 3

yw ... use that same process every time you solve using completing the square

Answer 4

@dumbcow ok can you help me with 2 things quick

Answer 5

sure

Answer 6

@dumbcow 1. explain if completing the square is a good method for solving when the discriminant is negative?

2. use h(x)=x^2+6x+12 as an example to justify your claim algebraicly and thanks again

Answer 7

well there are 2 methods for solving quadratics.... completing the square or quadratic formula

In either case if the discriminant is negative then no real solutions exist, solutions will be imaginary.

Answer 8

@dumbcow so you cant use the method

Answer 9

you can use either method, i dont know what they mean by asking if its a good method

Answer 10

@dumbcow ok what about #2

Answer 11

solve it the same way...

what is half of 6 squared?

Answer 12

@dumbcow would it be 18
cause 6^2 is 36 half of that is 18

Answer 13

no just like in the first problem
"x" coefficient was 8 ... we took half of 8, then squared it .... 4^2 = 16

here the "x" coefficient is 6 , half of 6, then square it ..... 3^2 = 9

Answer 14

@dumbcow then you just add it to both sides

Answer 15

yes

x^2 +6x + 9 = -12 + 9

Answer 16

@dumbcow ok now this is where im stuck now what do i do

Answer 17

look at the first example i did.

you have to factor left side, in general its always (x+b/2)^2 where "b" is middle coefficient

Answer 18

@dumbcow im sorry im confused on what you do next

Answer 19

do you remember factoring?

Answer 20

@dumbcow if i have to guess is it (x+6/2)^2
yes i do do you factor he number

Answer 21

right, but what is 6/2 ?

Answer 22

3

Answer 23

@dumbcow

Answer 24

(x+3)^2 = -3

Answer 25

o

Answer 26

@dumbcow now what do we do

Answer 27

we have (x+3)^2=-3

Answer 28

would it be x=-3

Answer 29

lol you didn;t understand my steps in the first problem huh

ok we had

(x-4)^2 = 4
then
x-4 = +-2

what operation cancels out a square?

Answer 30

divide?

Answer 31

nope

Answer 32

how would u do it

Answer 33

solve this

x^2 = 16

x = ?

Answer 34

x=4

Answer 35

how did you get that? what operation did you use on the 16

Answer 36

square root

Answer 37

there you go...to cancel out (x+3)^2 you have to take square root

Answer 38

so it would be x+3= im stuck now
@dumbcow

Answer 39

SQRT of -3

Answer 40

yep which is
\[\sqrt{3} i\]

Answer 41

sorry it should be plus or minus as well

Answer 42

so it equals \[x +3=\sqrt{3i}\]

Answer 43

+- before the SQRT

Answer 44

correct

Answer 45

oh ok great thank you @dumbcow

Answer 46

\[x = \pm i \sqrt{3} - 3\]

Answer 47

ok

Answer 48

@dumbcow have a good nighht thank you