Question 1208728
<pre>
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 ====> {{{matrix(1,3, 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? <font color = red><font size = 4><b>Well done!!</font></font></b></pre>