Solve the equation for x, where x is a real number (5 points): -2x^2 + 6x + 1 = -4

Add 4 to both sides so that the equation becomes -2x^2 + 6x + 5 = 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 = [ -6 ± √((6)^2 - 4(-2)(5)) ] / ( 2(-2) )
                                x = [-6 ± √(36 - (-40) ) ] / ( -4 )
                                x = [-6 ± √(76) ] / ( -4)
                                x = [-6 ± 2*sqrt(19) ] / ( -4 )
                                x = 3/2 ± -sqrt(19)/2
The answers are 3/2 + sqrt(19)/2 and 3/2 - sqrt(19)/2.

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