Question 30038
<pre>3x^2 - 2x - 3 = 0
Please help me solve this equation
<font size = 5><b>
By completing the square

3x² - 2x - 3 = 0

Get constant term on right by adding 3 to both sides

3x² - 2x = 3

Divide every term by the coefficient of x², namely 3


 3        2       3
--- x² - --- x = ---
 3        3       3

          2     
    x² - --- x = 1
          3
or written on one line

    x² - (2/3)x = 1

Multiply coefficient of x, -2/3 by 1/2, getting -1/3
Square -1/3:   (-1/3)2 = 1/9
Add 1/9 to both sides:

x² - (2/3)x + 1/9 = 1 + 1/9

The left side factors as

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

or

(x - 1/3)² = 1 + 1/9

The right side becomes 1 + 1/9 = 9/9 + 1/3 = 10/3

(x - 1/3)² = 10/9

Take the square root of both sides, remembering ± 
on the right side
            ____
x - 1/3 = ±<font face = "symbol">Ö</font>10/9
 
We can take the square root of denominator 9 as 3
            __
x - 1/3 = ±<font face = "symbol">Ö</font>10/3

Solving for x by adding 1/3 to both sides
           __
x = 1/3 ± <font face = "symbol">Ö</font>10/3

Both fractions have same denominator, so combine
numerators over the common denominator
          __
x = (1 ± <font face = "symbol">Ö</font>10)/3

Edwin
AnlytcPhil@aol.com</pre>