Solve the equation for x, where x is a real number (5 points): -4x^2 + 7x - 25 = 23

Subtract 23 from both sides so that the equation becomes -4x^2 + 7x - 48 = 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 = [ -7 ± √((7)^2 - 4(-4)(-48)) ] / ( 2(-4) )
                                      x = [-7 ± √(49 - (768) ) ] / ( -8 )
                                      x = [-7 ± √(-719) ] / ( -8)
Since √-719 is nonreal, the answer to this question is that there are no real solutions.