Question

0 = 4x^2 - 8x - 5

Answer 1

Do you know the quadratic formula?

Answer 2

\[\frac{ -(b) \pm \sqrt{(b)^{2}-(4)(a)(c)}}{ 2(a) }\]

Answer 3

yes, ive seen it, need help though

Answer 4

Where are you stuck then? The Quadratic formula works perfectly for quadratic equations

Answer 5

help me through it, I don't know how to do this

Answer 6

Divide every number by "4" then plug the new equation you have into the quadratic formula. Tell me when you have done this.

Answer 7

k

Answer 8

-5 cant be divided by 4

Answer 9

why can't it be divided 4?

Answer 10

or is it a = 4, b = -8 , c = -5 ?

Answer 11

You can do it that way if you want, if you have a harder time working with fractions.

Answer 12

I do

Answer 13

what do I do now, substitute my a, b, c into the formula?

Answer 14

yes

Answer 15

\[8 + \sqrt{-8^2 - 4(4)(-5) / 2(4)

Answer 16

Okay. I think you were trying to write this: \[\frac{ 8 \pm \sqrt{(-8)^{2} - 4(4)(-5)} }{ 2(4) }\]

Answer 17

yes

Answer 18

Alright. now do the math and find your two real answers.

Answer 19

\[8+\sqrt{64 +40}/8\]

Answer 20

is the 40 negative or positive?

Answer 21

oops its 80

Answer 22

well the equation inside reads as so:\[(-8)^{2}-4(4)(-5)\]

the second term will eventually become a negative and you're subtracting a negative. do you think it should be positive?

Answer 23

yes

Answer 24

good job. Now solve the rest of the math,

Answer 25

\[8+\sqrt{144/8}\]

Answer 26

do I have to divide?

Answer 27

the square root should only encompass the 144 not the division of 8 as that should be under the whole numerator as so:\[\frac{ 8 \pm \sqrt{144} }{ 8 }\]
do the square root first then do the numerator first for the "+" then the "-" and divide your numerators by your denominator to get your two answers

Answer 28

sqrt 144 is is 12

Answer 29

20/4 = 5

Answer 30

20/8***

Answer 31

right

Answer 32

20/8 = 2.5

Answer 33

is that it?

Answer 34

okay good job. But remember we're trying to solve for the variable "x" so how can we show that it equals 2.5

Answer 35

don't know

Answer 36

2.5 = x?

Answer 37

Yes. Another way you can show it in factor form is (x-2.5) since we're trying to find two factors that equals your quadratic equation. Now solve for your second one.

Answer 38

so how can i find the second factor?

Answer 39

you did your "+" one where is your "-" from your quadratic solution? Remember you ended up at:\[\frac{ 8\pm \sqrt{144} }{ 8 }\]

Answer 40

oh so now i subtract 8 - 12?

Answer 41

yes. when you see this sign:\[\pm\]it means "add" AND "subtract" the two terms on the two sides

Answer 42

oh ok, so 8 - 12 is -4

Answer 43

then divide -4/8 = -0.5

Answer 44

Awesome. Now how would you represent that in factored form?

Answer 45

that's the second factor (x - 0.5) ( x + 2.5)

Answer 46

( x + 2.5) (x - 0.5)

Answer 47

i think this is the factored form

Answer 48

No. remember that quadratic equation equals to "0" so when we use the quadratic formula we find any numbers that would make the quadratic equation equal to "0"

so with your first factor:
0 = (x - 2.5) which equals x = 2.5 since we moved the 2.5 to the other side by addition. we would also represent your second factor equaling to "0" since if we were to plug in the final number you received it would make the original quadratic equation "0" also.

0 = x + 0.5, we subtract 0.5 from each side to get x = -0.5 which was your answer right? so in factored form together these two will look like this

\[0 = (x-2.5)(x+0.5)\]

Answer 49

Another way to remember this is to change the sign of the number you get as your final answer to the opposite sign when putting it in factored form:

for example, if I were to get x = 5, and I want to put it into factored form. I would look at the number if it's either positive or negative. "5" here is positive so I changed it to negative so I can put it in factored form (x -5). This only applies when the quadratic equation is equal to "0"

Answer 50

oh i get it!!!! answer would be 0 = ( x -2.5) (x + 0.5)
Is that all?

Answer 51

Yes. That is all. Good work.

Answer 52

thank you so much!!!!!!!! :)