Question

Solve the equation for x, where x is a real number (5 points): -2x^2 + 7x + 21 = 16

Answer 1

Subtract 16 to both sides to the equation becomes -2x^2 + 7x + 5 = 0.

To solve this equation, we can make use of the quadratic formula. The quadratic formula solves equations of the form ax^2 + bx + c = 0
                                  x = [ -b ± √(b^2 - 4ac) ] / (2a)
                                  x = [ -7 ± √(7^2 - 4(-2)(5)) ] / ( 2(-2) )
                                  x = [ -7 ± √(49 - (-40) ) ] / ( -4 )
                                  x = [ -7 ± √(89) ] / ( -4)
                                  x = [ -7 ± sqrt(89) ] / ( -4 )
                                  x = 7/4 ± -sqrt(89)/4
The answers are 7/4 + sqrt(89)/4 and 7/4 - sqrt(89)/4.