Question

Solve: 0 = 6x2 − 10x − 4.

x = −1/3, x = −2

x = −1/3, x = 2

x = 1/3, x = −2

x = 1/3, x = 2

Answer 1

are you just looking for the answer or are you trying to learn the material?

Answer 2

learn

Answer 3

okay, do you know the quadratic equation?

Answer 4

nope

Answer 5

take a look here: http://www.mathsisfun.com/algebra/quadratic-equation.html

Answer 6

ok so the 2 squared makes it quadratic

Answer 7

the x^2 makes it quadratic, right. The general form is ax^2 + bx + c = 0. In your problem, what does that make the values of a, b, and c?

Answer 8

ax^2 + bx + c = 0
6^2 - 10x - 4 = 0

Answer 9

well you can't take the X out just yet, but just by inspecting the equation you should be able to see the values of A, B, and C. For example, C is -4 since it's the term without an X. can you tell me what A and B are?

Answer 10

start with 6x^2 - 10x - 4 = 0

Answer 11

A= 6x^2
B= -10x

Answer 12

a, b, and c are the terms that appear in front of the x^2 and x terms. For example, if the equation were

9x^2 + 4x - 8, then
a=9
b=4
c=-8

So, given that example, what numbers are A, B and C for your equation?

Answer 13

a=6
b=-12
c=-4

Answer 14

close -- you got A and C right, but not B, maybe just a typo?

Answer 15

ya srry -10

Answer 16

right! okay, now you have A, B and C so you can just plug them into the quadratic formula to get the two values of X that make the equation true. it's this: http://www.mathsisfun.com/algebra/images/quadratic-formula.gif

Answer 17

there may be two solutions, which you can find by using the "+" in the formula one time, and the "-" in the other time (where it says +/-)

Answer 18

i dont get this part

Answer 19

okay well you start with the quadratic formula, and every place you see A, B or C you substitute in the numbers for A B and C for your problem

Answer 20

_______________
x = -10 + / 10^2 - 46-4

Answer 21

_______________
x = -10 - / 10^2 - 46-4

Answer 22

well the first term in the top left is -b, and since for you b=-10, the negatives cancel so it's just 10

Answer 23

and (4)(a)(c) is 4 * 6 * -4

Answer 24

_______________
x = 10 + / 10^2 - 46-4

Answer 25

remember, "4ac" means 4 * a * c

Answer 26

_______________
x = 10 + / 10^2 - 4*6*4

Answer 27

and remember the division, it's all divided by 2a

Answer 28

then compute that and you'll get one of the two answers

Answer 29

2*6?
12

Answer 30

right, so put it all together and what answer do you get?

Answer 31

10+/10^2 -96

Answer 32

well remember 4 a c has a negative term in the c

Answer 33

so when you multiply it all out you get a negative number, which cancels with the negative in the equation

Answer 34

so just 96

Answer 35

right, so what's b^2 - 4 a c?

Answer 36

10^2 + 96

Answer 37

right, what does that add up to?

Answer 38

106^2

Answer 39

no...what's 10^2?

Answer 40

oh 100

Answer 41

so 196

Answer 42

right so what's 10^2 + 96?

Answer 43

and that's under a square root, so what's the square root of 196

Answer 44

14

Answer 45

yep so can you solve the whole quadratic formula now?

Answer 46

10 + / 14
-------- ???????????????
12

Answer 47

(10 + 14)/12 and (10 - 14)/12 are the two answers

Answer 48

note that the quadratic formula has a "+ or -" before the square root, meaning you do it once with + and a second time with - to get the two answers

Answer 49

ok so 24/12=1/2
and -4 / 12 = -3

Answer 50

close -- 24/12 = 2, not 1/2

Answer 51

the second answer you made the same mistake

Answer 52

oh sorry lol

Answer 53

i got 0.3333...

Answer 54

yeah, -1/3 is the right answer

Answer 55

ok so -1/3 and 2

Answer 56

check your multiple choices

Answer 57

yep

Answer 58

Why the quadratic formula?

Answer 59

so b

Answer 60

because it works in every case

Answer 61

yep, it's B

Answer 62

\[6x^2 - 10 x - 4 = 6x^2 - 12x + 2x - 4 = 6x(x - 2) + 2(x - 2) = (6x + 2)(x - 2)\cdots\]

Answer 63

Now the zero-product property.

Answer 64

why do that instead of the quadratic formula?

Answer 65

Because it is simpler

Answer 66

i disagree