Question

How do you solve using the completing the square method `3x^2 - 2x - 2 = 0`?

Answer 1

Isolate the x terms and complete the square.

Explanation:

First, we start by adding `2` to both sides to isolate the variable terms:
`3x^2-2x=2`

We can use the distributive property to take out a 3 from the left-hand side so we can make the coefficient of the `x^2` be 1:
`3(x^2-2/3x)=2`

Now, we can complete the square and simplify:
`3(x-1/3)^2-1/3=2`
`3(x-1/3)^2=2+1/3`
`3(x-1/3)^2=7/3`
`(x-1/3)^2=7/9`

Now, we square root both sides and solve for x:
`x-1/3=+-sqrt(7/9)`
`x-1/3=+-sqrt(7)/3`
`x=1/3+-sqrt(7)/3`
`x=(1+-sqrt(7))/3`

Therefore our solutions are: `x=(1+sqrt(7))/3,(1-sqrt(7))/3`