Question

4x squared+ 16=-24x Solve by completing the square

Answer 1

the first step in completing the square is to divide everything by the coefficient of x^2...so what is the coefficient of x^2?

Answer 2

No idea.

Answer 3

what is the number on the left side of x^2?

Answer 4

4

Answer 5

that's right! now divide every term by 4

Answer 6

Okay, so x^2+4=-6x?

Answer 7

yup :D

now...transpose all the x on one side and all the constants on the other

Answer 8

?

Answer 9

all the x on one side...all the numbers on the other...like

x^2 -x = 1 or something..can you do that?

Answer 10

So like x^2=4=-4 so x^2=-8?
-4 -4

Answer 11

Oops, x^2=-10?

Answer 12

no no...it's x^2 + 4 = -6x remember? you cannot combine 4 and 6x

Answer 13

So it's x^2=6x-4?

Answer 14

right..but bring -6x to the other side..put all the x on one side remember?

Answer 15

x^2=-6x-4 wait, can you combine 6x and x^2?
+6x +6x

Answer 16

no. you cannot..

so your equation becomes..x^2 + 6x = -4 right?

now here comes the good part...divide the coefficient of x (which is 6) by 2 then square it

Answer 17

So x^2=6x=-4 6x/2=3x 3x^2=9x?

Answer 18

no no...just the coefficient...just 6

Answer 19

so it becomes 9

Answer 20

Okay, but where does the coefficient come from?

Answer 21

how do I get the 6?

Answer 22

6x is the middle term right? the coefficient is the number on the left of the variable. the variable is x so the number on the left is 6. ok?

Answer 23

Okay.

Answer 24

Aren't there 2 possible answers, 9 & something else?

Answer 25

9 is not yet the answer...

you just have x^2 + 6x +9 = -4

then via law of equality because you added 9 on the left side..you need to add 9 on the right side so...

x^2 + 6x + 9 = -4 + 9

good?

Answer 26

yeah, so x^2+6x+9=5?

Answer 27

yes :DDD

now factor out x^2 + 6x + 9

Answer 28

Define factor out please, sorry I'm being so slow, I've been sick for a while, and as a result I have no idea what's going on, plus I usually get slightly ignorant when I'm sick, I assure you, I'm usually much better at Math.

Answer 29

x^2 + 6x + 9 is a perfect square trinomial..by factor out i mean change it to square of a binomial

Answer 30

I know what you're talking about, but my brain really doesn't want to work right now.

Answer 31

Hint: what was the number you squared a while ago?

Answer 32

6?

Answer 33

no...what is the square root of 9?

Answer 34

3

Answer 35

right! so the square of binomial is (x+3)^2

plug it in...

(x_3)^2 = 5

what do you think comes next?

Answer 36

4891

Answer 37

Lol, sorry, just being dumb. :P

Answer 38

4891? no...you take the square root of both sides. :)))

Answer 39

So (x-3)^2=5 x-3= Isn't the square root of 5 something like 2.2?

Answer 40

leave it as sqrt (5) but it's +/- remember

now transpose -3 and you're all done

Answer 41

How do I transpose -3?

Answer 42

x-3=sqrt(5) x=sqrt(5)+3
+3 +3