Solve the equation for x, where x is a real number (5 points): -5x^2 + 7x + 41 = 32

Subtract 32 to both sides to the equation becomes -5x^2 + 7x + 9 = 0.

To solve this equation, we can use the quadratic formula. The quadratic formula solves equations of the form ax^2 + bx + c = 0
                   x = [ -b ± √(b^2 - 4ac) ] / (2a)
                   x = [ -7 ± √(7^2 - 4(-5)(9)) ] / ( 2(-5) )
                   x = [ -7 ± √(49 - (-180) ) ] / ( -10 )
                   x = [ -7 ± √(229) ] / ( -10)
                   x = [ -7 ± sqrt(229) ] / ( -10 )
                   x = 7/10 ± -sqrt(229)/10
The answers are 7/10 + sqrt(229)/10 and 7/10 - sqrt(229)/10.