solve using the quadratic formula: 3x^2 - 2x -2=0?

Question

I would really appreciate the help. I checked out the website suggested and it was only more confusing.

Answer 1

x = [- b ± √ (b² - 4ac)] / 2a

a = 3, b = - 2 , c = -2

x = [ 2 ± √ (4 + 24 ) ] / 6

x = [ 2 ±√ 28 ] / 6

x = [ 2 ± 2√ 7 ] / 6

x = 1/3 ± (1/3).√ 7

x = 1/3.(1 ± √7 )

Answer 2

Since our equation is set equal to 0, we can start right in. Now, the quadratic formula is (-b±√b²-4ac))/2a.
Now, it's much less confusing if we use another formula along with this one that let's us know the values of the variables. That formula is ax²+bx+c=0, which is directly related to any quadratic formula (this formula is directly related to your formula 3x²-2x-2=0).
So, using this extra formula, we realize that a=3, because 3 is the number infront of x². b=-2, because +(-2)=-2, and -2 is the number infront of x. Finally, c=-2 because +(-2)=-2 and -2 is the number not attatced to an x term on the right side of the equation.
So, now we plug in these variables in the quadratic formula:

(-(-2)±√((-2)²-4(3*-2)))/2(3)

First off, we know that -(-2)=2. Next, since we have to use PEMDAS in the square root in the denominator, we simplify the parenthesis first. We know that (3*-2)=-6. Next, we know that (-2)²=4, and we know that -4(-6)=24. Finally, in the denominator, we see that 2(3)=6. Therefore our equation is now:

(2±√(4+24))/6.

Now, we know that 24+4=28, and, simplifying √28, we get 2√7. Therefore our equation is now:

(2±2√7)/6.

Therefore, your answer would be

2±2√7
----------
6

We then see that the highest number the whole numbers can be divided by is 2. Therefore, we divide both 2's and the 6 by 2, therefore getting our answer:

x=(1±√7)/3

There you go. I'm glad I could help. :)

Answer 3

-b plus or minus the squareroot of b^2 - 4ac divided by 2a
so a=3
b=-2
and c= -2

2 plus or minus the squareroot of -2^2 - 4(3)(-2)
divided bye a(3)

2 plus or minus square root of 4 +24 divides by 6

2 +/- square root of 28 divided by 6

2 + 5.29150262 divided by 6 and
2 - 5.29150262 divided by 6

3.29150262 divided by 6
7.29150262 divided by 6

ANSWERS:
0.54858377
and
1.21525044

i think

Answer 4

[-b +/- square root ( b^2-4ac)]/2a
a=3 b=-2 c=-2
[2+/- sqrt(4+24)]/6
[2+ sqrt 28]/6 or [2- sqrt 28]/6
(2+5.3)/6= 1.2 or (2- 5.3)/6 = -0.55
the closest answer after pluggin the x's is -0.55

Answer 5

(3x-1)(x + 2)=0

x= -1/3 or x = -2

Answer 6

ax^2 + bx + c =

x = (-b +/- sqrt(b^2-4ac) )/2a

a = 3, b = -2, c = -2

Answer 7

x= [-(-2)+/-√(4-(4*3*(-2))]/6
x=[2+/-√(4+24)]/6
x=[2+/-2√7]/6

Answer 8

x=-(-2)+/-[(4+24)^1/2]/9
=2/6+/-2/6rt7
=1/3(1+rt7);1/3(1-rt7)