To find the value of x + ½ from the expression -2(1-2x)(x-1)-(2x-1), we can simplify the expression first by using the distributive property and then combining like terms.

Starting with the expression:

-2(1-2x)(x-1)-(2x-1)

First, we can expand the expression inside the parentheses using the distributive property:

-2(1-2x)(x-1) = -2(x(x-1)-2x(1-1)) = -2(x^2-x)

Then, we can substitute this expression back into the original expression:

-2(x^2-x)-(2x-1)

Next, we can distribute the negative sign to both terms inside the parentheses:

-2x^2 + 2x - 2x + 1

Simplifying further by combining like terms, we get:

-2x^2 + 1

Now, we can set this expression equal to x + ½ and solve for x:

-2x^2 + 1 = x + ½

Rearranging this equation, we get a quadratic equation in standard form:

2x^2 - x - 1/2 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac))/(2a)

where a = 2, b = -1, and c = -1/2.

Plugging in these values, we get:

x = (-(-1) ± sqrt((-1)^2 - 4(2)(-1/2)))/(2(2))

x = (1 ± sqrt(5))/4

Therefore, the value of x + ½ is:

x + ½ = (1 ± sqrt(5))/4 + 1/2

x + ½ = (1 ± sqrt(5))/4 + 2/4

x + ½ = (1 ± sqrt(5) + 2)/4

x + ½ = (3 ± sqrt(5))/4

So, the two possible values of x + ½ are (3 + sqrt(5))/4 and (3 - sqrt(5))/4.