Question

Solve for x. Enter your answer in interval notation using grouping symbols.

x^2+4x<45

Answer 1

(-9,5)

Answer 2

http://www.wolframalpha.com/input/?i=x^2%2B4x%3C45

Answer 3

First set the one side equal to 0. Subtracting 45 from both sides we get:

x^2+4x-45<0.

Then factor it, just like you would an equation. That means making two binomials and using guess and check or the multiplication method. We find it will factor to:

(x+9)(x-5)<0

Then we set each part equal to 0 and solve to find the 'zeroes':

x+9=0 and x-5=0
x=-9 and x=5

The rule for quadratic inequalities, found here: http://www.mathwarehouse.com/quadratic-inequality/how-to-solve-and-graph-quadratic-inequality.php says that we take these values and place the lowest one to the left and the other one to the right of x.

So, -9<x<5, but we want it in interval form which would be:

(-9,5)