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Completing the Square

Completing the Square. Solving Quadratics By Completing the Square Part 2. Must be a perfect Square. Perfect Square On One side. Review Solve for x. Take Square Root of BOTH SIDES. When you take the square root, You MUST consider the Positive and Negative answers.

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Completing the Square

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  1. Completing the Square Solving Quadratics By Completing the Square Part 2 Must be a perfect Square

  2. Perfect Square On One side Review Solve for x Take Square Root of BOTH SIDES When you take the square root, You MUST consider the Positive and Negative answers.

  3. Perfect Square On One side Solve for x Take Square Root of BOTH SIDES But what happens if you DON’T have a perfect square on one side……. You make it a Perfect Square Use the relations on next slide…

  4. Short Cut To expand a perfect square binomial: We can use these relations to find the missing term….To make it a perfect square trinomial that can be factored into a perfect square binomial. Then

  5. Make this a perfect square trinomial • Take ½ middle term • Then square it • The resulting trinomial is called a perfect square trinomial, • which can be factored into a perfect square binomial.

  6. Make one side a perfect square • Add a blank to both sides • Divide “b” by 2 • 4. Square that answer. • Add it to both sides • Factor 1st side • Square root both sides • Solve for x Solve by completing the square 1.

  7. Short cut! Factor this Perfect square trinomial Bring down sign What is the Square root of x2 What is the Square root of 36

  8. Move constant to other side. • Add a blank to both sides • Divide “b” by 2 • 4. Square that answer. • Add it to both sides • Factor 1st side • Square root both sides • Solve for x Solve by completing the square 2. -8 -8

  9. Short cut! Factor this Perfect square trinomial Bring down sign What is the Square root of x2 What is the Square root of 9

  10. Move constant to other side. • Add a blank to both sides • Divide “b” by 2 • Square that answer. • Add it to both sides • Factor 1st side • Square root both sides • Solve for x Solve by completing the square 3. +84 +84

  11. Short cut! Factor this Perfect square trinomial Bring down sign What is the Square root of x2 What is the Square root of 9

  12. Move constant to other side. • Add a blank to both sides • Divide “b” by 2 • Square that answer. • Add it to both sides • Factor 1st side • Square root both sides • Solve for x Solve by completing the square 4. +15 +15

  13. Short cut! Factor this Perfect square trinomial Bring down sign What is the Square root of x2 What is the Square root of 9

  14. Move the constant to side by itself. Make the side (w/variables) a perfect square by adding a certain number to both sides. To calculate this number Divide “b” (middle term) by 2 Then square that answer Take the square root of both sides of eq Then solve for x Steps to solve Quadratics by completing the square:

  15. In a perfect square, there is a relationship between the coefficient of the middle term and the constant term.

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