Test a value from each interval to see if it satisfies the original inequality.
Step 1
We will start by solving the related equation.
- 12 = - 5x^2-10x ⇔ 5x^2+ 10x+( - 12)=0We see above that a= 5, b= 10, and c= - 12. 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=- 10±sqrt(340)/10
x=- 10 + sqrt(340)/10
x=- 10 - sqrt(340)/10
x=- 10/10+sqrt(340)/10
x=- 10/10-sqrt(340)/10
x≈ 0.84
x≈ - 2.84
Step 2
The solutions of the related equation are approximately - 2.84 and 0.84. 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 < - 2.84. For simplicity, we will choose x=- 4.
