Test a value from each interval to see if it satisfies the original inequality.
Step 1
We will start by solving the related equation.
- 1=- x^2-5x ⇔ 1x^2+ 5x+( - 1)=0We see above that a= 1, b= 5, and c= - 1. 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=- 5±sqrt(29)/2
x=- 5 + sqrt(29)/2
x=- 5 - sqrt(29)/2
x=- 5/2+sqrt(29)/2
x=- 5/2-sqrt(29)/2
x≈ 0.19
x≈ - 5.19
Step 2
The solutions of the related equation are approximately - 5.19 and 0.19. Let's plot them on a number line. Since the original is not a strict inequality, the points will be closed.
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 ≤ - 5.19. For simplicity, we will choose x=- 10.
