Identifying the Algebraic Elements of Completing the Square
by the Application of Areas

• Left Click Check Button.

• Counting From the Rightmost Gold Bead, Left Click a Gold Bead at a position equal any Number. Click  Right Arrow (CRA). This step generates (B), which equals the displaced gold beads. Let B" designate B-squared.

• Left click another  gold  beads in or out of the displaced group (B). CRA. This step generates (a), the bead clicked  plus the total number of gold beads to its right.

• Left click another  gold bead in any group. CRA. This step generates (e), the bead clicked in step 4 plus the total number of gold beads to its right, while (f) equals (B)-(e) while (f) equals (B)-(e)

•  C1 the third term of the equation will equal the areas that elbow around an area equal a quadrant of B". These areas will share corners at the intersection of the red lines
• Or C1 will equal areas of a quadrant of B"that elbows around the area of the square with a shared corner at the intersection of red lines and its the opposite corner at the intersection of yellow lines.
• Below you will Click Down Arrow (PDA) to enter numbers in equations.
• And you will Click Up Arrow (PUA) to enter variables.
• PDA twice.
• C2 the third term of the equation equal (0) will equal the areas  that elbow around an area equal a quadrant of B". These areas will share corners at the intersection of the green lines
• Or C2 will equal areas of a quadrant of B"that elbows around the area of the square with a shared corner at the intersection of the green lines and its opposite corner at the intersection of the yellow lines.