Question

3x^2-7x-3=0

Answer 1

3times3 is 9 which doesnt factor into 7.... so quadratic it :)

Answer 2

after using the quadratic formula, how do you complete the problem?

Answer 3

that is the completed problem.

you could try doing the "complete the square" method; but all that method does is prove that the quad formula works.

Answer 4

my textbook says to find the nearest degree.. x = sin of theta

Answer 5

then find what x equals and take the sine inverse of it. the inverse trig funtions take numbers for inputs and spit back angles. Does that make sense?

Answer 6

not really :/

Answer 7

lets walk you thru it then :)

first get the values for x with the quad formula.

7/6 (+-) sqrt(49-(4)(-3)(3))/ 6

7/6 (+-) sqrt(49+36)/6

7/6 (+-) sqrt(85)/6

you with me so far?

Answer 8

ok, let me see.

Answer 9

where do you get 49?

Answer 10

the quad form reads:

-middle (+-) sqrt(middle^2 -4(first)(last)) all over 2(first).

or more formally:

-b (+-) sqrt(b^2-4(a)(c))
---------------------
2(a)

right?

-7 times -7 = 49

Answer 11

oh. it's b^2? no wonder i never got any solution out of that. thank you very much!

+5

Answer 12

we got numbers for our x now; (7/6 (+-) sqrt(85)/6) if I did it correctly right?

Answer 13

umm.. i'm still solving it. i got the b^2 correct

Answer 14

my calculator says -49 instead of 49. so weird～

Answer 15

lol.... maybe user error?

To find out what sin(t) is when x equals some number we write it like this:

sin(t) = x

To find out what "t" is we need to get rid of the (sin) part. And we do that by using what is called the sine inverse function.

Answer 16

i think it was supposed to be 7 not -7

Answer 17

all it changes in the end is the sign of (7/6) to (-7/6) which may or may not be an issue

Answer 18

got it.
\[x=7\pm \sqrt{49+36} \div 6\]

Answer 19

if your equation you gave was correct, then it was supposed to be (-7)^2 = 49. But (7)^2 = 49 just the same

Answer 20

good :) you ready to learn about sin inverse? its symbol is (sin^-1)

Answer 21

i know sin^-1 but i'm stuck in where should i go next.

Answer 22

lets walk it thru. It asks us to find sin(t) = x right?

Answer 23

sin \[\theta\]

Answer 24

theta is simply a name, I will make it simpler and just name it "t" do you think I can do that?

Answer 25

yea, sure. :)

Answer 26

lol...good, mathmaticians like to rename things all the time, makes them feel important :)

Answer 27

XD

Answer 28

we have:

sin(t) = x

we need to get rid of the "sin" part. So lets apply sin^-1 to each side to get:

t = sin^-1(x)

Now plug the numbers into your scientific calculator to get an angle for t, formally known as theta

Answer 29

wait. i'm confused here. do i continue with the quad. formula?

Answer 30

the quad formula simply gave us the values for x....its job is done and it can go take a well deserved break...

Answer 31

so i continue with this:\[3\sin^2\theta-7\sin \theta-3=0\]

Answer 32

aha!!! you were holding back vital information...hmmm

Answer 33

opps.. am i in trouble?

Answer 34

nah....just makes the problem more understandable now :)

Answer 35

XD. so how do i continue?

Answer 36

just the same as before :)

sin(t) = x and solve for t

But I gotta tell wonder, do you have the problem written correctly becuase I get some wierd stuff when I plug it into the calculator..

Answer 37

the textbook says to use the quadratic formula to find,to the nearest degree, all values of theta in the interval 0 degrees [less than or equal to] theta [less than] 360 degrees that satisfy each equation.

Answer 38

338.29 degrees is what I get, which is in Quad4 but it is also hiding in Quad3 under the disguise of 201.71 degrees.

Answer 39

[7+sqrt(85)] /6 is greater then 1 so it spits out an error.

x = 2.7 and that aint between -1 and 1 so it is a false reading.

Answer 40

[7-sqrt(85)]/6 = -0.3699 which IS between -1 and 1 so it is a good value of x.

Answer 41

is there anyway to verify the answer?

Answer 42

i got the same answer as you. -0.3699240762

Answer 43

either were both geniuses or were both idiots...take your pick :)

Answer 44

GENIUS! :D

Answer 45

yay!!!

Answer 46

the thing about sin^-1 is that it only gives an angle that is on the right hand side of a circle. So you have to remember to look over to the other sid eto see where it matches up at.

Answer 47

does any of that make sense to you?

Answer 48

somewhat, let me think over~

Answer 49

i think i got it, thanks for helping me though(: