Answer:
x = (-3 + sqrt(23)i) / 2 and x = (-3 - sqrt(23)i) / 2.
Explanation:
To solve the quadratic equation -x^2 + 3x - 8 = 0, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation.
In this case, a = -1, b = 3, and c = -8. Substituting into the quadratic formula, we get:
x = (-3 ± sqrt(3^2 - 4(-1)(-8))) / 2(-1)
Simplifying the expression inside the square root:
x = (-3 ± sqrt(9 - 32)) / (-2)
x = (-3 ± sqrt(-23)) / (-2)
Since the square root of a negative number is not a real number, the solutions to this quadratic equation are complex numbers. We can simplify the expression by writing the solutions in terms of the imaginary unit i:
x = (-3 ± sqrt(23)i) / 2
Therefore, the solutions to the quadratic equation -x^2 + 3x - 8 = 0 are x = (-3 + sqrt(23)i) / 2 and x = (-3 - sqrt(23)i) / 2.