SOLVE BY COMPLETING THE SQUARE:

2X - 24 = -2X²

First get all terms containing X on the left side
and the number term on the right. Make sure the term
containing X² comes first on the left:

2X² + 2X = 24

Divide through by the coefficient of X², which is 2:

2X²/2 + 2X/2 = 24/2

      X² + X = 12

Multiply the coefficient of X, which is 1 by 1/2.
This gives 1/2.  Now square this result, which
gives 1/4.  Now add +1/4 to both sides of the equation:

X² + X + 1/4 = 12 + 1/4

Factor the left side as (X + 1/2)(X + 1/2) or (X + 1/2)²

(X + 1/2)² = 12 + 1/4

Combine the terms on the right:

(X + 1/2)² = 49/4

Take the square roots of both sides:
             ____
 X + 1/2 = ±Ö49/4

 X + 1/2 = ±7/2

Add -1/2 to both sides:

       X = -1/2 ± 7/2

Using the +

       X = -1/2 + 7/2 = 6/2 = 3

Using the -

       X = -1/2 - 7/2 = -8/2 = -4

Edwin