Question

How do you solve `3x(x+2)=2` using the quadratic formula?

Answer 1

Convert the given equation to the form of a quadratic equation, `ax^2+bx+c=0`. Identify a, b, and c. Substitute the values into the quadratic formula `x=(-b+-sqrt(b^2-4ac))/(2a)`, and solve for x. There will be two solutions for x.

Explanation:

The equation needs to be in the form `ax^2+bx+c=0`.

`3x(x+2)=2`

`3x^2+6x=2`

`3x^2+6x-2=0`

Quadratic Formula

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

`a=3;` `b=6;` `c=-2`

`x=(-6+-sqrt(6^2-4*3*-2))/(2*3)`

`x=(-6+-sqrt(36+24))/(6)`

`x=(-6+-sqrt(60))/6`

`sqrt(60)=sqrt(4xx15)=2sqrt 15`

`x=(-6+-2sqrt15)/6`

`x=-1+(2sqrt 15)/3`

`x=-1-(2sqrt15)/3`