Question

Solve: 3x^2 + 16x - 9 = 3

Answer 1

@jim_thompson5910

Answer 2

I'll get you started

3x^2 + 16x - 9 = 3

3x^2 + 16x - 9 - 3 = 0

3x^2 + 16x - 12 = 0

Now use the quadratic formula to solve for x

Answer 3

oh right! thank you @jim_thompson5910

Answer 4

tell me what you get so I can check your answer

Answer 5

ok im doing it now

Answer 6

just to verify the equation its -16x +/- the square root of (16)^2-4(3)(-12)/2(3) correct?

Answer 7

Solving 3x2+16x-12 = 0 by the Quadratic Formula

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC
x = ————————
2A

In our case, A = 3
B = 16
C = -12

Accordingly, B2 - 4AC =
256 - (-144) =
400

Applying the quadratic formula :

-16 ± √ 400
x = ——————
6

Can √ 400 be simplified ?

The prime factorization of 400 is
2•2•2•2•5•5
To be able to remove something from under the radical, there have to be 2 instances of it because we are taking a square i.e. 2nd root.

√ 400 = √ 2•2•2•2•5•5 =2•2•5•√ 1 =
± 20 • √ 1 =
± 20

So now we are looking at:
x = ( -16 ± 20) / 6

Two real solutions:

x =(-16+√400)/6 = u solve
or:
x =(-16-√400)/6 = u solve then i'll check to see if u get the concept :)

Answer 8

i got
-16-\[\sqrt{-2928}\]
all over 6 but idk if that is the final answer

Answer 9

x =(-16-√400)/6 = (-8-10)/3 =

x =(-16+√400)/6 = (-8+10)/3 =

Let me simplify, see if u can get it!

Answer 10

@xokatexo do you need further help in understanding the concept?

Answer 11

is that the final answer?

Answer 12

The quadratic formula should "work" fine here, but I've found it easier to "factor by grouping."

\[3x ^{2}+16x-2=3x ^{2}=18x-2x-2=3x(x+6)-2(x+6).\]

Answer 13

No, u have to simplify that to find the final two solutions. I mean maybe i'm not explaining this right, sorry I'm better at solving then explaining. Are there any terms that can't be simplified ? no so u can simplify :)

Answer 14

so my answer wasnt right

Answer 15

where did you get 400 from @Nanalew

Answer 16

(x+6) is the common factor here. Factoring it out, we get (x+6)(3x-2)=0.
What are the solutions of that?

Answer 17

Two real solutions:

x =(-16+√400)/6 = (-8+10)/3 = 0.66667
or:
x =(-16-√400)/6 = (-8-10)/3 = -6.00000

Here maybe understanding the answer will help u understand the problem. :D

Answer 18

@mathmale i think im supposed to use the quadratic formula

Answer 19

@Nanalew so this is what i did

Answer 20

OK, so be it. Good luck!

Answer 21

@agent0smith can u help me explain, i don't think I'm getting this concept across plus ur really good at explaining

Answer 22

Be certain to use the quadratic formula on 3x^2+16x-12=0.

Answer 23

3x^2+16x-9=3
-3 -3
---------------
3x^2 +16x-12=0

-b+/- the square root of b^2-4ac
--------------------------------
2a

-16 +/- the square root of (16)^2-4(3)(-12)
--------------------------------------
6

Answer 24

Let @xokatexo be the judge of that.

Answer 25

then i got -16+/- the square root of -2928
----------------------------
6
as my answer

Answer 26

Sorry, but something's 'way off here.

Whoever got 400 under the radical of the quadratic formula was correct.

\[x=\frac{ -16+\sqrt{400} }{ 6 }\]
is one solution. What is the other?

Answer 27

okay i see where your coming from, here maybe @mathmale is on the right track it is easier to solve this way.. Simplify 3x2+16x-9 - 3

Trying to factor by splitting the middle term
Factoring 3x2+16x-12

The first term is, 3x2 its coefficient is 3
The middle term is, +16x its coefficient is 16
The last term, "the constant", is -12

Step-1 : Multiply the coefficient of the first term by the constant 3 • -12 = -36

Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is 16

-36 + 1 = -35
-18 + 2 = -16
-12 + 3 = -9
-9 + 4 = -5
-6 + 6 = 0
-4 + 9 = 5
-3 + 12 = 9
-2 + 18 = 16
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, (-2) and (18)
3x2 - 2x + 18x - 12

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x-2)
Add up the last 2 terms, pulling out common factors :
6 • (3x-2)
Now add up the four terms of step 3 :
(x+6) • (3x-2)
Solve

2.2 Solve : 3x-2 = 0

Add 2 to both sides of the equation :
3x = 2
Divide both sides of the equation by 3:
x = 2/3

Solving a Single Variable Equation :

2.3 Solve : x+6 = 0

Subtract 6 from both sides of the equation :
x = -6

See two solutions, is this easier to understand. It can be solved multiple ways :)

Answer 28

Remember: "order of operations" is extremely important. Under the radical sign you have the following expression:\[16^{2}-4(3)(-12).\]

Answer 29

According to "order of operations," we MUST multiply and/or divide BEFORE we add or subtract. Therefore, evaluate 4(3)(-12) BEFORE subtracting the result from 16^2.
Try it.

Answer 30

@xokatexo : I hope you're still with us!

Answer 31

yeah i am im trying to do it that way

Answer 32

Do my methods not make sense??

Answer 33

its 256-144

Answer 34

So, the radicand (the number under the square root operator) is .... ????
@xokatexo , you're on the right track except for a sign error. Mind going back and checking?

Answer 35

OHHH okay i got it

Answer 36

omg thanks so much wow ididnt pay attention to the other negative to make it positive

Answer 37

ohhh when solving the quadratic formula here re-look at this step!! Accordingly, B2 - 4AC =
256 - (-144) =
400
now look back at the problem :)

Answer 38

so its -16 + the square root of 400
-------------------------
6

Answer 39

I'm so glad y ou've both gotten the correct result!
Now, would you please find the two solutions? x1=? x2=?

Answer 40

YESSS ! :) let me repost :)


Solving 3x2+16x-12 = 0 by the Quadratic Formula

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC
x = ————————
2A

In our case, A = 3
B = 16
C = -12

Accordingly, B2 - 4AC =
256 - (-144) =
400

Applying the quadratic formula :

-16 ± √ 400
x = ——————
6

Can √ 400 be simplified ?

The prime factorization of 400 is
2•2•2•2•5•5
To be able to remove something from under the radical, there have to be 2 instances of it because we are taking a square i.e. 2nd root.

√ 400 = √ 2•2•2•2•5•5 =2•2•5•√ 1 =
± 20 • √ 1 =
± 20

So now we are looking at:
x = ( -16 ± 20) / 6

Two real solutions:
x =(-16+√400)/6 = (-8+10)/3 = 0.66667
or:
x =(-16-√400)/6 = (-8-10)/3 = -6.00000

see now complete problem, do u understand ?

Answer 41

\[-16+\sqrt{400}\]
----------------
6

Answer 42

and then -

Answer 43

actually thank you so much you both helped me so much!!!!!!

Answer 44

My great pleasure. Come back soon!

Answer 45

medal?

Answer 46

Awwww, Nanalew! We help others just through the goodness of our hearts, don't we? :)

Answer 47

ugh i cant give you both medals but i became fans!!

Answer 48

thanks @mathmale u helped me explain, here i medal u too. plus i worked really hard.... did u see my posts..... tell me u don't enjoy a reward for helping jeesh

Answer 49

I'm just ribbing you. I'm not telling you not to enjoy a well-earned reward! :)

Answer 50

yeah u seriously helped @mathmale, if u hadn't pointed out @xokatexo hadn't use order of operations i would have gone on babbling haha and yes i get it now, i'm still struggling w/ english so forgive me for not understanding humor

Answer 51

happy to help and good luck to everyone :)

Answer 52

@xokatexo make sure you follow order of operations, because this is colossally wrong and will cause you a lot of trouble in algebra

For evaluating: (16)^2-4(3)(-12)

you did:

16^2 =256
256-4=252
252(-36)=-9072

http://www.mathsisfun.com/operation-order-pemdas.html

Answer 53

yeah thanks!! idk i usually do im just blanking today haha

Answer 54

Thanks @agent0smith u r the best at explaining ! :D

Answer 55

thanks though!!!!