SOLUTION: Solve by completing the square. x^2 + (2/3)x - 1/3 = 0 Let me see. x^2 + (2\3)x = 1/3 [(2/3) ÷ 2]^2 = 1/9 x^2 + (2/3)x + 1/9 = 1/3 + 1/9 x^2 + (2/3)x + 1/9

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Question 1208728: Solve by completing the square.

x^2 + (2/3)x - 1/3 = 0

Let me see.
x^2 + (2\3)x = 1/3
[(2/3) ÷ 2]^2 = 1/9
x^2 + (2/3)x + 1/9 = 1/3 + 1/9
x^2 + (2/3)x + 1/9 = 4/9
(x + 1/3) (x + 1/3) = 4/9
(x + 1/3)^2 = 4/9
Taking the square square on both sides, I get
x + 1/3 = 2/3 & x + 1/3 = -2/3
Now solve for x by setting x + 1/3 to equal 2/3 and then -2/3.
x + 1/3 = 2/3
x = 2/3 - 1/3
x = 1/3
And
x + 1/3 = -2/3
x = -2/3 - 1/3
x = -3/3
x = -1
You say?
Found 2 solutions by timofer, MathTherapy:
Answer by timofer(105)   (Show Source): You can put this solution on YOUR website!
The numeric term which completes the square is .


May go like this...











either -1 or +1/3
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Solve by completing the square.

x^

Let me see.

x^2 + (2\3)x = 1/3

[(2/3) ÷ 2]^2 = 1/9

x^2 + (2/3)x + 1/9  = 1/3 + 1/9

x^2 + (2/3)x + 1/9 = 4/9

(x +  1/3) (x + 1/3) = 4/9

(x + 1/3)^2 = 4/9

Taking the square square on both sides, I get 

x + 1/3 = 2/3 & x + 1/3 = -2/3

Now solve for x by setting x + 1/3 to equal 2/3 and then -2/3. 

x + 1/3 = 2/3

x = 2/3 - 1/3

x = 1/3

And 

x + 1/3 = -2/3

x = -2/3 - 1/3

x = -3/3

x = -1

You say?


x^2 + (2\3)x = 1/3 ====>  

                   ====> [(2/3) ÷ 2]^2 = 1/9 <==== CORRECT

x^2 + (2/3)x + 1/9  = 1/3 + 1/9 <===== CORRECT

x^2 + (2/3)x + 1/9 = 4/9 <===== CORRECT

(x +  1/3)(x + 1/3) = 4/9 <==== CORRECT, but in MY OPINION, not necessary

(x + 1/3)^2 = 4/9 <==== CORRECT

Taking the square square on both sides, I get 

x + 1/3 = 2/3 & x + 1/3 = -2/3 <====== CORRECT

Now solve for x by setting x + 1/3 to equal 2/3 and then -2/3. 

x + 1/3 = 2/3

x = 2/3 - 1/3

x = 1/3 <===== CORRECT

And 

x + 1/3 = -2/3

x = -2/3 - 1/3

x = -3/3

x = -1 <====== CORRECT

You say? Well done!!
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