Question

How do you solve `x^2-8x+3=0` using the quadratic formula?

Answer 1

`x = 7.605` and `x= 0.395`

Explanation:

I'll show the quadratic formula down below so we can use that as a reference:

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 `-8x`, and `c` is a number by itself. It would be 3 for this question.

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

`x = (- (-8) +- sqrt((-8)^(2) - 4(1)(3)))/(2(1))`

`x = (8 +-sqrt(64-12))/2`

`x = (8 +- 7.21)/2`

For these type of problems, you will obtain two solutions because of the `+-` part. So what you want to do is add 8 and 7.21 together and divide that by 2:

`x = (8+7.21)/2`
`x = 15.21/2= 7.605`

Now, we subtract 7.21 from 8 and divide by 2:

`x = (8-7.21)/2`
`x = 0.79/2 = 0.395`

Therefore, the two possible solutions are:
`x = 7.605` and `x = 0.395`