Question

How do you solve `x^2+3x+2=0` using the quadratic formula?

Answer 1

The two solutions are `x = -1` and `x = -2`

Explanation:

Since this question is given in standard form, meaning that it follows the form: `ax^(2) + bx + c = 0`, we can use the quadratic formula to solve for x:

I think it's worthwhile to mention that `a` is the number that has the `x^2` term associated with it. Thus, it would be `1x^(2)` for this question. `b` is the number that has the `x` variable associated with it and it would be `3x`, and `c` is a number by itself and in this case it is 2.

Now, we just plug our values into the equation like this:

`x = (- (3) +- sqrt((3)^(2) - 4(1)(2)))/(2(1))`

`x = (-3 +-sqrt(9-8))/2`

`x = (-3 +- sqrt(1))/2`

For these type of problems, you will obtain two solutions because of the `+-` part. So what you want to do is add -3 and `sqrt(1)` together and divide that by 2:

`x = (-3+sqrt(1))/2`
`x = -2/2= -1`

Now, we subtract `sqrt(1)` from -3 and divide that by 2:

`x = (-3-sqrt(1))/2`
`x = -4/2 = -2`

Therefore, the two possible solutions are:
`x = -1` and `x = -2`