Solve: 3x2 + 2x + 1 = 1.
We need to rewrite the equation so it has zero on one side. Subtract 1 from each side to find
3x2 + 2x = 0.
Now we plug the numbers
into the quadratic formula to find
The solutions are
In this instance, we could also have found the solutions by factoring, since
3x2 + 2x = x(3x + 2)
Thankfully, we get the same solutions whether we factor or use the quadratic formula. Once again, we are assured that all is right in the mathematical universe. Boy, we'll sleep well tonight.