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