Question

Solve the equation for x, where x is a real number (5 points): -3x^2 + 6x + 9 = 7

Answer 1

Add -7 to both sides so that the equation becomes -3x^2 + 6x + 2 = 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(-3)(2)) ] / ( 2(-3) )
                                       x = [-6 ± √(36 - (-24) ) ] / ( -6 )
                                       x = [-6 ± √(60) ] / ( -6)
                                       x = [-6 ± 2*sqrt(15) ] / ( -6 )
                                       x = 1 ± -sqrt(15)/3
The answers are 1 + sqrt(15)/3 and 1 - sqrt(15)/3.