Question

How do you solve `x(x+6)=-2` using the quadratic formula?

Answer 1

When given an equation of the form, `ax^2+bx+c = 0`, one can find the value(s) of x by substituting the values for a, b, and c into the quadratic formula:

`x = (-b+-sqrt(b^2-4(a)(c)))/(2a)`

Explanation:

The given equation `x(x+6)=-2` is not in the form specified in the answer, therefore, we must put it in that form.

Use the distributive property on the left side:

`x^2 + 6x = -2`

Add 2 to both sides:

`x^2 + 6x +2= 0`

By observation, `a = 1, b = 6, and c = 2`

Substitute these values into the quadratic formula:

`x = (-6+-sqrt(6^2-4(1)(2)))/(2(1))`

`x = (-6+-sqrt(36-8))/2`

`x = (-6+-sqrt(28))/2`

`x = (-6+-2sqrt7)/2`

`x = -3+-sqrt7`

`x = -3-sqrt7` and `x = -3+sqrt7`