Test a value from each interval to see if it satisfies the original inequality.
Step 1
We will start by solving the related equation.
x^2+6x = - 5 ⇔ 1x^2+ 6x+ 5=0We see above that a= 1, b= 6, and c= 5. Let's substitute these values into the Quadratic Formula to solve the equation.
Now we can calculate the first root using the positive sign and the second root using the negative sign.
x = - 6 ± 4/2
x = - 6 + 4/2
x = - 6 - 4/2
x = - 2/2
x = - 10/2
x = - 1
x = - 5
Step 2
The solutions of the related equation are - 1 and - 5. Let's plot them on a number line. Since the original is a strict inequality, the points will be open.
Step 3
Finally, we must test a value from each interval to see if it satisfies the original inequality. Let's choose a value from the first interval, x < - 5. For simplicity, we will choose x=- 6.
