Question

Use the quadratic formula to solve the equation. If necessary round to the nearest hundredth.
x^2+3=-4x

Answer 1

OK, what's the quadratic equation? And do you have the problem in the correct form to use it?

Answer 2

I don't know what the quadratic equation is

Answer 3

Or if its in the correct form

Answer 4

Seems lie you are on a bad path, trying to answer problems when you have not learned the material. Quadratic equation is a foundation in math.
Hang on.

Answer 5

Ok

Answer 6

Sorry, I meant the quadratic _formula_.

Answer 7

i know

Answer 8

Quadratic formula is a shortcut to finding answers to problems, when the _form_ of the problem is a*x^2 + b*x + c = 0.

Answer 9

So what do I do then?

Answer 10

Do you have enough algebra to put your problem into this format, and tell me what a, b, and c are, while I the next step ready?

Answer 11

a-0.02
b-2.3
c-6

Answer 12

its already in that format

Answer 13

Well, no it isn't in that form. There is a '-4x' on the right side of the equal sign, and in the format, there is supposed to be a '0' on the right side and all the x^2 and x terms on the left. and none of your a,b,c are correct.

Is this the equation we are working on:
x^2 + 3 = -4x ???

Answer 14

yeah i was wrong

Answer 15

oh

Answer 16

wait idk

Answer 17

u had the right equation I didn't lol

Answer 18

NP. how can we move the '4x' part over the left side?

Answer 19

subtract?

Answer 20

on both sides

Answer 21

Sure. Just be careful with signs, we are subtracting 'negative four x' from both sides, like this:

x^2 + 3 = -4x
x^2 + 3 - (-4x) = (-4x) - (-4x)

Your turn. Finish up the math on this step and let me know.

Answer 22

x^2+3-(-4x)=0

Answer 23

Now, what can you do when you have two minus signs in a row, like in '-(-4x)' ?

Answer 24

make it positive

Answer 25

Then put the terms in the right order: X^2 first, then x , then constants (numbers without any x).

Answer 26

and wite it all out for us

Answer 27

x^2+4x+3=0

Answer 28

is that right?

Answer 29

Yep, so tell me what a, b, and c are, while I the next step ready.

Answer 30

a-x^2
b-4x
c-3

Answer 31

Sorry to take so long between some answers, my connection is really crazy today.

Answer 32

Its ok

Answer 33

Close, but look again at the format: a*x^2 + b*x + c = 0
a does not include the x^2 part, and b does not include the x part.

Answer 34

a-1
b-4
c-3

Answer 35

Next step uses this formula to get the answers:\[x= \frac{ -b \pm \sqrt{b ^{2} - 4ac} }{ 2a }\]

Just want to check, do you know what \[\sqrt{(something)}\] and \[\pm (something)\] mean?

Answer 36

top one is square root don't know the bottom

Answer 37

NP. Correct on square root, that is the tough one.

The other, it looks like you stitched together a 'plus' sign and a 'minus' sign, and that is exactly what it means. It means the formula has to be used twice, once like this:\[x= \frac{ -b + \sqrt{b ^{2} - 4ac} }{ 2a }\] and again like this: \[x= \frac{ -b - \sqrt{b ^{2} - 4ac} }{ 2a }\]

Answer 38

ugh

Answer 39

I know. For algebra, quadratic formula is about as messy as it gets. Lots of work.

Answer 40

You go plug in those numbers, and I'll do my copy, and we'll check your answers.

Answer 41

\[-4x \pm \sqrt{4^2-4(1*3)}\]

Answer 42

over 2(1)

Answer 43

Did you leave the 'x' in by mistake? Otherwise, yes, correct.

Answer 44

yea

Answer 45

Now what?

Answer 46

NP, we are trying to speak three 'languages', between math formulas and English and keyboarding!

Finish the math and I can check your work!

Answer 47

ok

Answer 48

-7.6

Answer 49

Because we have an x^2, term, there will _always_ be two possible answers.
(with two exceptions. Sometimes the part under the square root sign is equal to zero, and so you really have the same answer twice. And sometimes the part under the square root is negative, and the two answers have imaginary numbers. But not this day.)
You should have two real answers here.

Answer 50

(-4+ ___)/2 and (-4 - ___)/2 ??

Answer 51

idk im officially lost

Answer 52

Sorry. Ignore my long paragraph two comments back for now.

Take my word for it, this problem will have two answers.
Let's go back to the part where you gave me \[x= \frac{ -4 \pm \sqrt{4 ^{2} - 4(1)(3)} }{ 2(1) }\]

Answer 53

\[x= \frac{ -4 \pm \sqrt{4 ^{2} - 12} }{ 2 }\]

One answer (call it x1, or x-sub-one), is: \[x_{1}= \frac{ -4 + \sqrt{4 ^{2} - 12} }{ 2 }\] The other is:\[x_{2}= \frac{ -4 - \sqrt{4 ^{2} - 12} }{ 2 }\]

Answer 54

My lunch break is over and I have to go. When you get your answers, try to put them back into the original equation x^2+3=-4x and see if both sides of the equation are equal.