1/2 x^2 - 1/3 x - 1/6 = 0 solve by factoring? ?

Multiply equation by 6.

3x² - 2x - 1 = 0

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

x=1, -1/3

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

3x+1 = 0, x=-1/3
x-1 = 0, x=1


..

x 6
3x^2 - 2x - 1 = 0
(3x+1)(x-1) = 0

x = 1 or -1/3

1/6 ( 3x^2 -2x - 1) = 0
1/6 (3x+1)(x-1) = 0

x = - 1/3 OR x=1

situation a million A = 3/2(B-a million) 2/3A = B – a million 2/3A + a million = B Rectangle situation Width + 5 = length, enable W = Width and L = length and A = section W + 5 = L or W = L - 5 (W)(L) = A, when you consider which you prefer L, replace W with L – 5 (L – 5)(L) = sixty six L^2 – 5L -sixty six = 0, then sparkling up by way of utilising the quadratic equation and you get L = (5 ±17)/2 or L = 6 or 11 yet if you consider that W = L – 5, W must be a million or 6. To get sixty six sq. meters, the only values of L and W that provide that are L = 11 and W = 6 answer: L = 11

3x² - 2x - 1 = 0
(3x + 1)(x - 1) = 0
x = - 1/3 , x = 1

Case 1.
(1/2)x^2-(1/2)x-1/6=0=>
[3x^2-2x-1]/6=0=>
(x-1)(3x+1)=0=>
x=1 or x=-1/3

case 2
1/(2x^2)-1/(3x)-1/6=0=>
[3-2x-x^2]/(6x^2)=0=>
x^2+2x-3=0 (assuming x<>0)=>
(x+3)(x-1)=0=>
x=-3 or x=1

1/2(x^2) - 1/3(x) - 1/6 = 0
x^2/2 - x/3 - 1/6 = 0
6(x^2/2 - x/3 - 1/6) = 6(0)
3x^2 - 2x - 1 = 0
3x^2 + x - 3x - 1 = 0
(3x^2 + x) - (3x + 1) = 0
x(3x + 1) - 1(3x + 1) = 0
(3x + 1)(x - 1) = 0

3x + 1 = 0
3x = -1
x = -1/3

x - 1 = 0
x = 1

∴ x = -1/3 , 1

( -1/6 + k ) ( -1/6 - k) = (1/2)(-1/6)
1/36 - k^2 = -1/12
1/36 + 1/12 = k^2
4/36 = k^2
2/6 = k
1/3 = k

-1/6 + 1/3 = 3/18 = 1/6
-1/6 - 1/3 = -9/18 = -1/2

1/2 x^2 - 1/2 x + 1/6 x - 1/6 = 0
(1/2 x) (x - 1) + (1/6) (x - 1) = 0
(1/2 x + 1/6) ( x - 1) = 0

1/2 x = -1/6
x = -1/3

or

x = 1

1/2 x^2 - 1/3 x - 1/6 = 0 : original
Multiply everything by 6 to clear fractions
= 3x^2 - 2x - 1 = 0
Now factor to (3x + 1)(x - 1)
So x = -1/3 or x = 1