# How do you solve and write the following in interval notation: x^2+9x+20≥2?

May 30, 2016

Start by solving as a regular quadratic equation (we change the inequality sign to an equal for the time being).

${x}^{2} + 9 x + 20 = 2$

${x}^{2} + 9 x + 18 = 0$

$\left(x + 6\right) \left(x + 3\right) = 0$

$x = - 6 \mathmr{and} - 3$

Now, we select test points that are at different segments of the number line representation of this inequality, as shown below.

BLUE SEGMENT: Let the test point be $x = - 8$

Testing:

(-8)^2 + 9(-8) + 20 >=^? 2

$64 - 72 + 20 \ge 2$, therefore this interval satisfies the equation. This instantly means that the pink segment is not a solution to the inequality while the green is. Quick checks yield the same result.

Therefore, in interval notation, the solution set is $\left(- \infty , - 6\right) \bigcup \left(- 3 , \infty\right)$

Hopefully this helps!