The sum of a number and 20 is no more than the sum of the square of the number and 9

Translate the given statement into an inequality:

x+20 is less than or equal to x^2+9.  Solve for x.

Subtract x+20 from both sides of this inequality.  We get 0 is less than or equal to x^2+9-x-20, or 

0 is less than or equal to x^2-x-11

Temporarily set x^2-x-11 = to 0 and solve for x:

Using the quadratic formula with a=1, b=-1 and c=-11, 

      -(-1) plus or minus sqrt([-1]^2-4(1)(-11))
x=
                                  2(1)
       1 plus or minus sqrt(45)
  =
                      2
         1 plus or minus 3sqrt(5)
  =  
                       2

Evaluate these two results and plot them on a number line.  Based upon these results (values), write inequalities to represent the distinct intervals:

(-infinity,a), (a,b), (b, infinity

Determine which interval or intervals contain x values that make the given inequality true.

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