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.