Factor the equation x 2-x plus 5 0 justify your answer?

To factor the equation ( x^2 - x + 5 = 0 ), we first check the discriminant ( b^2 - 4ac ) where ( a = 1 ), ( b = -1 ), and ( c = 5 ). The discriminant is ( (-1)^2 - 4(1)(5) = 1 - 20 = -19 ), which is negative. This indicates that the equation has no real roots and cannot be factored over the real numbers. However, it can be expressed in terms of complex roots if necessary.