Question

How do you solve `7x^2+2x-2=0` using the quadratic formula?

Answer 1

`x= (-1+-sqrt(15))/7`

Explanation:

Given a quadratic equationin the form:
`color(white)("XXX")color(red)(a)x^2+color(blue)(b)x+color(green)(c) = 0`
the quadratic formula tells us that the solutions are:
`color(white)("XXX")x= (-color(blue)(b)+-sqrt(color(blue)(b)^2-4color(red)(a)color(green)(c)))/(2color(red)(a))`

Given
`color(white)("XXX")color(red)(7)x^2+color(blue)(2)x+color(green)(-2)`
this becomes
`color(white)("XXX")x= (-color(blue)(2)+-sqrt(color(blue)(2)^2-4 * color(red)(7) * color(green)((-2))))/(2 * color(red)(7))`

`color(white)("XXXXX")= (-1+-sqrt(15))/7`