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

1 Answer
May 10, 2017

Answer:

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#