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10.5 Solving Quadratic Equations By Completing the Square

10.5 Solving Quadratic Equations By Completing the Square. Review Square Root Method. Use if there is no linear term. (i.e. B = 0) Get the Quadratic Term on one side and the Constant on the other side. Simply take the Square Root of Both Sides. Square Root Method.

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10.5 Solving Quadratic Equations By Completing the Square

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  1. 10.5 Solving Quadratic Equations By Completing the Square

  2. Review Square Root Method • Use if there is no linear term. (i.e. B = 0) • Get the Quadratic Term on one side and the Constant on the other side. • Simply take the Square Root of Both Sides.

  3. Square Root Method Be sure to give both the positive and negative answers!

  4. Solving Quadratic Equations by Completing the Square Goal: Turn the problem into a Square Root Problem

  5. Completing the Square • Take HALF the coefficient of the linear term (i.e. B ) and square. • Example: x2 + 8x + c • Example: x2 + 12x + c • Example: x2 + 9x + c c = 16 c = 36 c = 81/4

  6. Find the value of c that makes a perfect square. Then write the trinomial as a perfect square. Step 1 Find one half of 16. Step 2 Square the result of Step 1. Step 3 Add the result of Step 2 to Answer:The trinomial can be written as Example 4-3a

  7. Find the value of c that makes a perfect square. Then write the trinomial as a perfect square. Example 4-3b Answer: 9; (x + 3)2

  8. Solve by completing the square. Notice that is not a perfect square. Rewrite so the left side is of the form Since add 4 to each side. Write the left side as a perfect square by factoring. Example 4-4a

  9. Square Root Property Subtract 2 from each side. Write as two equations. or Solve each equation. Example 4-4a Answer: The solution set is {–6, 2}.

  10. Solve by completing the square. Example 4-4b Answer:{–6, 1}

  11. Solve by completing the square. Notice thatis not a perfect square. Divide by the coefficient of the quadratic term, 3. Add to each side. Since add to each side. Example 4-5a

  12. Write the left side as a perfect square by factoring. Simplify the right side. Square Root Property Add to each side. Example 4-5a

  13. Solve each equation. Answer: The solution set is Write as two equations. or Example 4-5a

  14. Example 4-5b Classwork/Homework

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