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+12x=28 ⇔ - 1x^2+ 12x+( - 28)=0We see above that a= - 1, b= 12, and c= - 28. 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=- 12±sqrt(32)/- 2
x=- 12 + sqrt(32)/- 2
x=- 12 - sqrt(32)/- 2
x=- 12/- 2 + sqrt(32)/- 2
x=- 12/- 2 - sqrt(32)/- 2
x=6-sqrt(32)/2
x=6+sqrt(32)/2
x≈ 3.17
x≈ 8.83
Step 2
The solutions of the related equation are approximately 3.17 and 8.83. 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 ≤ 3.17. For simplicity, we will choose x=0.
