4x2 + x = - 3 how do people get an "i" term?

4x² + x = - 3

You need to use the quadratic formula to solve this. First make sure to get everything on one side so the equation equals 0.

4x² + x + 3 = 0

x = (-b + / - √b² - 4ac) / 2a

x = (-1 + / - √1² - 4 (4) (3)) / 2 (4)

x = (-1 + / - √1 - 48) / 8

x = (-1 + / - √-47) / 8

Now before you continue, remember that you can't have a negative number in the square root. √-47 is the same as √47 * √-1.

√-1 is the same thing as i, so you can take that out.

It will now look like this: i√47

So now you can continue doing the problem.

x = (-1 + / - i√47) / 8

x = - 1/8 + / - (i√47) / 8

This can't really be simplified further.

So if you are meant to put it in a + bi form, then the answers would be:

x = - 1/8 + (i√47) / 8

x = - 1/8 - (i√47) / 8