X2-4/8- 2x+3/3=-1

To solve the equation, we will start by simplifying both sides of the equation.

First, let's simplify the left side of the equation:

x^2 - (4/8) - 2x + (3/3) = -1

Since 4/8 can be simplified to 1/2 and 3/3 is equal to 1, we have:

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

Next, let's combine the like terms:

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

We can simplify further by finding a common denominator for the fractions:

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

This gives us:

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

Simplifying the fractions:

x^2 - 2x + 4/2 = -1

x^2 - 2x + 2 = -1

Now, let's move all the terms to one side of the equation:

x^2 - 2x + 2 + 1 = 0

x^2 - 2x + 3 = 0

At this point, we have a quadratic equation. To solve it, we can either factor, complete the square, or use the quadratic formula. However, this specific quadratic equation cannot be easily factored, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 1, b = -2, and c = 3. Plugging in these values, we have:

x = (-(-2) ± √((-2)^2 - 4(1)(3))) / (2(1))

Simplifying:

x = (2 ± √(4 - 12)) / 2

x = (2 ± √(-8)) / 2

At this point, we notice that the square root of a negative number is not a real number. Therefore, the solution to the equation is not a real number.