Question

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

Answer 1

Subtract 5 to both sides so that the equation becomes -2x^2 + 6x - 1 = 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)(-1)) ] / ( 2(-2) )
                                            x = [-6 ± √(36 - (8) ) ] / ( -4 )
                                            x = [-6 ± √(28) ] / (-4)
                                            x = [-6 ± 2*sqrt(7) ] / (-4 )
                                            x =3/2 ± -sqrt(7)/ 2
The answers are 3/2 + sqrt(7)/2 and 3/2 - sqrt(7)/2.