Test a value from each interval to see if it satisfies the original inequality.
Step 1
We will start by solving the related equation.
- 11 = - 2x^2-5x ⇔ 2x^2+ 5x+( - 11)=0We see above that a= 2, b= 5, and c= - 11. 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(113)/4
x=- 5 + sqrt(113)/4
x=- 5 - sqrt(113)/4
x=- 5/4+sqrt(113)/4
x=- 5/4-sqrt(113)/4
x≈ 1.41
x≈ - 3.91
Step 2
The solutions of the related equation are approximately - 3.91 and 1.41. 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 ≤ - 3.91. For simplicity, we will choose x=- 4.
