Start with the general quadratic equation:

 Ax² + Bx + C = 0

Subtract C from both sides

     Ax² + Bx = -C

Divide through by A

    x² + x = 

Simplify:

     x² + x = 

                                   Multiply the coefficient of x by :   = 
                                   Square .   = 
                                   Add  to both sides:

x² + x +  =  - 

Factor the left side and get LCD of 4A² on the right

(x + )(x + ) =  - 

Write left side as the square of a binomial.  Multiply fractions on far right

(x + )² =  - 

Combine fractions on the right over the LCD

(x + )² =  

Use the principle of square roots:

x +  = 

Take square roots of top and bottom on the right:

x +  = 

x +  = 

Add  to both sides:

               x =  ± 

Combine the fractions on the right over 2A

               x = 


Edwin