Question

I am lost. Can someone please show me (step-by-step because I need this for future reference) how to solve this problem using quadratic formula? Thank you in advance! (will post question in comments area)

Answer 1

do you know the quadratic formula?

Answer 2

Sorry, OS crashed @triciaal Yes ma'am I know the formula and how to apply it. Here are the steps I made it through:

\[4k^2+4k-14=0\]
\[\frac{ -4+/- \sqrt{4^2-4(4)(-14)} }{ 2(4) }\]
\[\frac{ -4+/ \sqrt{16 + 224} }{ 8 }\]
\[\frac{ -4+/- \sqrt{240} }{ 8 }\]

Now I cannot figure out what to do next in order to get an answer that matches the answer choices.

Answer 3

240 isn't a perfect square root
but we can simplify it
factor 240
one of the factors should be the perfect square root (meaning when u take square root u should get perfect number not decimal )

Answer 4

I found that it has
4 * 60 (4 is the sqrt)
15 *16 (16 being a square root)

Just not sure how to proceed from here

Answer 5

alright yes 16 times 15 looks good to me \[\large\rm \frac{ -4 \pm \sqrt{16 * 15} }{ 8 }\]take square root of 16
\[\large\rm \frac{ -4 \pm 4\sqrt{ 15} }{ 8 }\] now take out the common factor from the numerator

Answer 6

would I take out a 2 or a 4 ? because they have both

Answer 7

we always take GCF (greatest common factor )

Answer 8

ok (i ddnt know that so I will write it down!) Do it do it in the bottom also to get -->
\[\frac{ -1+/- \sqrt{15} }{ 2 }\]

Or should I keep it as an 8 ?

Answer 9

how did you get 2 at the denominator ? :=))

Answer 10

I divided 8 /4 (which was the GCF up top)

Answer 11

4 is at the top so divide 4/8 \[\frac{ 4(-1 \pm \sqrt{15} )}{ 8 }\]
and then reduce the 4/8 fraction would get 8 or 2 at the bottom ?

Answer 12

would you*

Answer 13

no i meant i divided the top by 4 and the bottom by 4 (because 4 was the GCF)

Answer 14

the system was down

Answer 15

yes you made it to B

Answer 16

ye as usual triciaal. :(
you can continue now!!!

Answer 17

once you identify your a,b,c substitute in the formula and simplify

Answer 18

ahh i see when we take out gcf we basically divide
so to take out 4 from (-4 pm 4{15}) you should divide the numerator by 4 not the denominator

Answer 19

you divide both

Answer 20

\[\frac{ 4(\frac{-4}{4} \pm \frac{4\sqrt{15}}{4} )}{ 8 } \rightarrow \frac{4(-1 \pm \sqrt{15})}{8}\]
now you can reduce 4/8 fraction

Answer 21

Okay, I know what the answer is now, I believe it is A :)

Answer 22

look again

Answer 23

ah i seee. you will get the same answer

Answer 24

you can divide both numerator and denominator by gcf

Answer 25

oh wait, i forgot to add the negative sign! the answer is B

that tricky little negative sign was tryna pull a fast one on me!

Answer 26

or if you read the thread I said it above

Answer 27

Yes i seen where you said "look again" and i looked and noticed i forgot to put the negative sign, thanks! for all of the help yall!

Answer 28

you are welcome