Test a value from each interval to see if it satisfies the original inequality.
Step 1
We will start by solving the related equation.
- 3 = - x^2-4x ⇔ 1x^2+ 4x+( - 3)=0We see above that a= 1, b= 4, and c= - 3. 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=- 4±sqrt(28)/2
x=- 4 + sqrt(28)/2
x=- 4 - sqrt(28)/2
x=- 4/2+sqrt(28)/2
x=- 4/2-sqrt(28)/2
x≈ 0.65
x≈ - 4.65
Step 2
The solutions of the related equation are approximately - 4.65 and 0.65 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 ≤ - 4.65. For simplicity, we will choose x=- 5.
