What are the possible values of x in -11x^2 + 2x = 10?

        -11x² + 2x = 10
-11x² + 2x - 10 = 10 - 10
-11x² + 2x - 10 = 0
x = -(2) +/- √((2)² - 4(-11)(-10))
                     2(-11)
x = -2 +/- √(4 - 440)
               -22
x = -2 +/- √(-436)
             -22
x = -2 +/- 2i√(109)
              -22
x = -2 + 2i√(109)        x = -2 - 2i√(109)
             -22                            -22
x = ¹/₁₁ - ¹/₁₁i√(109)    x = ¹/₁₁ + ¹/₁₁i√(109)

Since x can be any real number the domain is (-infinity,infinity)

 

To find the range we need to find the vertex of the parabola which is at (-b/2a , y)

-b/2a would be 2/2 = 1 ... so find the y value at x = 1

12 - 2(1) - 15 = 1-17 = -16

So the vertex is at (1,-16)

Since the parabola opens upward from that point the minimum value of the range is y = -16

The range would include the point -16 so it is actually

R = [-16,infinity)