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Completing the Square – Demonstration

Explore animated demonstrations of this mathematical method. Learn to rewrite expressions to simplify solving quadratic equations. Practice manipulating coefficients for a symmetric result. Master the technique and improve problem-solving skills.

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Completing the Square – Demonstration

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  1. Completing the Square – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

  2. The area of this rectangle is 40 m2. Can you calculate the value of ? This is difficult to solve because appears twice. If we manipulate the expression so there is only one , it is easier. Trial & Error? The area of the whole square = But we only want the shaded area, so we must subtract the white area. This can be solved without a calculator.

  3. The area of this rectangle is 40 m2. Can you calculate the value of ? But length must be positive. meters This is called Completing the Square. We use it on quadratic equations to make them symmetrical (with one ) so finding an answer is easier.

  4. Completing the Square DEMO Model these expressions and rewrite them so there is only one instance of . Can you write a rule for completing the square?

  5. Completing the Square DEMO Model these expressions and rewrite them so there is only one instance of . Can you write a rule for completing the square?

  6. Completing the Square DEMO Rewrite in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 16 to get the original expression.

  7. Completing the Square DEMO Rewrite in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 9 to get the original expression.

  8. Completing the Square DEMO Rewrite in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 25 to get the original expression.

  9. Completing the Square DEMO Rewrite in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 1 to get the original expression.

  10. Completing the Square DEMO Rewrite in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 4 to get the original expression.

  11. Completing the Square DEMO Rewrite in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 36 to get the original expression.

  12. Completing the Square DEMO YOUR TURN Rewrite Rewrite in the form in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 9 to get the original expression.

  13. Completing the Square DEMO YOUR TURN Rewrite Rewrite in the form in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 9 to get the original expression.

  14. Completing the Square DEMO Rewrite in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 5 to get +4.

  15. Completing the Square DEMO Rewrite in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 11 to get +5.

  16. Completing the Square DEMO Rewrite in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 18 to get +7.

  17. Completing the Square DEMO Rewrite in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 11 to get −1.

  18. Completing the Square DEMO YOUR TURN Rewrite Rewrite in the form in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 11 to get +5.

  19. Completing the Square DEMO YOUR TURN Rewrite Rewrite in the form in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 11 to get +5.

  20. Completing the Square DEMO YOUR TURN Rewrite Rewrite in the form in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 11 to get +5.

  21. Completing the Square DEMO YOUR TURN Rewrite these expressions in the form: Rewrite in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 11 to get +5.

  22. Completing the Square DEMO YOUR TURN Rewrite these expressions in the form: Rewrite in the form 1) Halve the coefficient of and place into a squared bracket. 2) Expand the brackets to calculate how you need to adjust the expression. We need to subtract 11 to get +5.

  23. Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths.co.uk

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