Solve the equation for x, where x is a real number (5 points): -11x^2 + 5x - 3 = 0

To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
                   x = [ -b ± √(b^2 - 4ac) ] / (2a)
                   x = [ -5 ± √((5)^2 - 4(-11)(-3)) ] / ( 2(-11) )
                   x = [-5 ± √(25 - (132) ) ] / ( -22 )
                   x = [-5 ± √(-107) ] / ( -22)
Since we conclude that √-107 is nonreal, the answer to this question is that there are no real solutions.