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

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Answer 1 · 2017-05-10T01:22:40

Isolate the x terms and complete the square.

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: $x=(1+sqrt(7))/3,(1-sqrt(7))/3$

How do you solve using the completing the square method 3x^2 - 2x - 2 = 03x^2 - 2x - 2 = 0?