Question

Solve the equation for x, where x is a real number (5 points):

Answer 1

Subtract sqrt(3) to both sides so that the equation becomes -3x^2 + 7x + 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 = [ -7 ± √((7)^2 - 4(-3)(2)) ] / ( 2(-3) )
                             x = [-7 ± √(49 - (-24) ) ] / ( -6 )
                             x = [-7 ± √(73) ] / ( -6)
                             x = [-7 ± sqrt(73) ] / ( -6 )
                             x = 7/6 ± -sqrt(73)/6
The answers are 7/6 + sqrt(73)/6 and 7/6 - sqrt(73)/6.