6.4 solve quadratic equations by completing the square

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6.4 solve quadratic equations by completing the square

  1. 1. Solving Quadratic Equations by Completing the Square
  2. 2. Perfect Square Trinomials <ul><li>Examples </li></ul><ul><li>x 2 + 6x + 9 </li></ul><ul><li>x 2 - 10x + 25 </li></ul><ul><li>x 2 + 12x + 36 </li></ul>
  3. 3. Creating a Perfect Square Trinomial <ul><li>In the following perfect square trinomial, the constant term is missing. X 2 + 14x + ____ </li></ul><ul><li>Find the constant term by squaring half the coefficient of the linear term. </li></ul><ul><li>(14/2) 2 X 2 + 14x + 49 </li></ul>
  4. 4. Perfect Square Trinomials <ul><li>Create perfect square trinomials. </li></ul><ul><li>x 2 + 20x + ___ </li></ul><ul><li>x 2 - 4x + ___ </li></ul><ul><li>x 2 + 5x + ___ </li></ul>100 4 25/4
  5. 5. Solving Quadratic Equations by Completing the Square <ul><li>Solve the following equation by completing the square: </li></ul><ul><li>Step 1: Move quadratic term, and linear term to left side of the equation </li></ul>
  6. 6. Solving Quadratic Equations by Completing the Square <ul><li>Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. </li></ul>
  7. 7. Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.
  8. 8. Solving Quadratic Equations by Completing the Square <ul><li>Step 4: Take the square root of each side </li></ul>
  9. 9. Solving Quadratic Equations by Completing the Square <ul><li>Step 5: Set up the two possibilities and solve </li></ul>
  10. 10. Completing the Square-Example #2 <ul><li>Solve the following equation by completing the square: </li></ul><ul><li>Step 1: Move quadratic term, and linear term to left side of the equation, the constant to the right side of the equation. </li></ul>
  11. 11. Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. The quadratic coefficient must be equal to 1 before you complete the square, so you must divide all terms by the quadratic coefficient first.
  12. 12. Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.
  13. 13. Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side
  14. 14. Solving Quadratic Equations by Completing the Square Try the following examples. Do your work on your paper and then check your answers.

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