Question

Solve the equation for x, where x is a real number (5 points): 2x^2 + 9x - 1 = 3

Answer 1

Subtract 3 from both sides so that the equation becomes 2x^2 + 9x - 4 = 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 = [ -9 ± √(9^2 - 4(2)(-4)) ] / ( 2(2) )
                                 x = [ -9 ± √(81 - (-32) ) ] / ( 4 )
                                 x = [ -9 ± √(113) ] / ( 4)
                                 x = [ -9 ± sqrt(113) ] / ( 4 )
                                 x = -9/4 ± sqrt(113)/4
The answers are -9/4 + sqrt(113)/4 and -9/4 - sqrt(113)/4.