i need help with this problem 3x^2 + x - 1/2 = 0 (3x squared)?

Question

Math help!!!

the answer is x+7 over 6 and x-7 over 6. How do i get that?!

Answer 1

6x² + 2x - 1 = 0
x = [ - 2 ± √(4 + 24) ] / 12
x = [ - 2 ± √(28) ] / 12
x = [ - 2 ± 2√7 ] / 12
x = [ - 1 ± √(7) ] / 6

Answer 2

hint: Use the quadratic formula to remedy those which you won't be able to factor. Given ax² + bx + c = 0, quadratic formula: x = [-b ± ?(b²-4ac)]/2a x²-5x+2=0 a = a million, b = -5, c = 2 x = [-b ± ?(b²-4ac)]/2a x = [5 ± ?(a million²-4(a million)(2))]/2(a million) x = [5 ± ?(a million-8)]/2 x = [5 ± ?(-7)]/2 x = [5 ± i?7]/2 x²+3x-7=0 a = a million, b = 3, c = -7 x = [-b ± ?(b²-4ac)]/2a x = [-3 ± ?(a million²-4(a million)(-7))]/2(a million) x = [-3 ± ?(a million+28)]/2 x = [-3 ± ?29]/2 2x²-5x+2=0 (2x-a million)(x-2) = 0 x = a million/2 or 2 2x²-3x-5=0 (2x-5)(x+a million) = 0 x = 5/2 or -a million 3x²+5x+a million=0 a = 3, b = 5, c = a million x = [-b ± ?(b²-4ac)]/2a x = [-5 ± ?(5²-4(3)(a million))]/2(3) x = [-5 ± ?(25-12)]/6 x = [-5 ± ?13]/6

Answer 3

Ok this is a quadratic and consequently there are two ways to go about solving it.
1. Factor
2. use quadratic formula.

I think that in this case it is easier to use the formual..

[-b+- square root (b^2 - 4ac)] / 2a
where a= 3, b= 1, c= -1/2

plug in the values and you get;

[-1+ square root ((-1)^2 - 4(3)(-1/2))]/ 2(3)
[-1 + square root (7)] / 6

and the negative,
[-1 - square root (7)] / 6

hmmm... I hope this helps.

Answer 4

you can either use the quadratic formula as suggested by everyone else or you could complete the square.

either way you get x=[-1(+/-)sqrt(7)]/6.

to complete the square:

3x^2+x-1/2=0...move the constant to the other side
3x^2+x=1/2...divide by coefficient of x^2 (3)
x^2+(1/3)x=1/6...take half of the coefficient of x,
square it and add it to both sides.
x^2+1/3x+1/36=7/36...factor the left side
(x+1/6)^2=7/36...square root of both sides
x+1/6=(+/-)sqrt(7)/6...subtract 1/6 from both sides
x=[-1(+/-)sqrt(7)]/6

Answer 5

You can only solve through using the quadratic formula (listed above). a=3, b=1, c=1/2. Since there is no factor where (3)(-1/2) can equal 1, the quadratic equation is only way.

Answer 6

use the quadratic formula
x=-b+-(b*b-4*a*c)^1/2/2a (i hope u understand the equation)
where b=1;a=3;c=-1/2

Answer 7

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

Answer 8

Use the quadratic equation as above.

Answer 9

x = [ -b + or - (b^2 - 4ac)^1/2 ] / 2a

2 answers 1st x= 0.27429
2nd x = -0.60763

Answer 10

x=(-1 + SQRT(7))/6 ~ 0.27
x=(-1 - SQRT(7))/6 ~ -0.61