180 likes | 382 Views
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.
E N D
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 Be sure to give both the positive and negative answers!
Solving Quadratic Equations by Completing the Square Goal: Turn the problem into a Square Root Problem
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
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
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
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
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}.
Solve by completing the square. Example 4-4b Answer:{–6, 1}
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
Write the left side as a perfect square by factoring. Simplify the right side. Square Root Property Add to each side. Example 4-5a
Solve each equation. Answer: The solution set is Write as two equations. or Example 4-5a
Example 4-5b Classwork/Homework