Question

How do you solve `x^2 +6x +8 =0` using the quadratic formula?

Answer 1

The answers are `x=-2` and `x=-4`.

Explanation:

To start, the quadratic formula is `x=(-bpmsqrt(b^2-4ac))/(2a)`

In this problem, `a = 1` (as the `x^2` term has no coefficient), `b=6`, and `c=8`.

Plug those values into the quadratic equation to get:

`x=(-6pmsqrt(6^2-4(1)(8)))/(2(1))`

Multiply `2*1` on the bottom of the fraction:

`x=(-6pmsqrt(6^2-4(1)(8)))/(2)`

Square `6` and multiply `4*1*8` within the square root:

`x=(-6pmsqrt(36-32))/(2)`

Subtract `36-32` inside the root:

`x=(-6pmsqrt(4))/(2)`

Solve for `sqrt(4)`

`x=(-6pm2)/(2)`

If the `pm` is positive, you get

`x=(-6+2)/(2)`, which simplifies to `x=(-4)/(2)`, or `color(red)(-2)`

If the `pm` is negative, you get

`x=(-6-2)/(2)`, which simplifies to `x=(-8)/(2)`, or `color(red)(-4)`

Answer 2

x = -2 or x = -4

Explanation:

The quadratic formula looks like
`x = (-b +- sqrt(b^2 - 4ac))/(2a)`

You have...
`ax^2 + bx + c = 0`
and your equation...
`x^2 + 6x +8 = 0`

With that you can do...
`x^2 +6x + 8 = 0`
`a = 1`
`b = 6`
`c = 8`

Then you substitute what you have into the quadratic formula
When you do that you get...
`x = (-(6) +- sqrt((6)^2 - 4(1)(8)))/(2(a))`

The '`+-`' means that your going to have 2 answers like x = this or that so, you can just solve the whole equation using '`+`' first then use '`-`' next.

when you do that you'll get an answer of `x = -2 or -4`