Completing the Square to Solve a Quadratic

1. Completing the Square to Solve a Quadratic

2. Completing the Square: A new Way to Solve Quadratics We have seen how to solve the equation below by taking the square root: But, this method only works if the equation is identical to the one above (a perfect square trinomial equals a number). It would be useful to learn how to rewrite an equation (like the one below) so it is identical to the one above. Then, you can apply the square root technique.

3. Completing the Square to Solve a Quadratic Solve: Try to make a Square with the tiles Complete the square by adding the unit tiles needed to make a perfect square to both sides. = Never complete the square by adding additional variables Since there is one x, you can square root to solve Factor the perfect square trinomial

4. Perfect Square A polynomial that can be factored into the following form: (x + a)2 Examples:

5. Completing the Square x2 + bx + c is a perfect square if: (The value of c will always be positive.) Ex: Prove the following is a perfect square Half of b=-16 squared is 64=c

6. Completing the Square Find the c that completes the square: • x2 + 50x + c • x2 – 22x + c • x2 + 15x + c

7. Factoring a Completed Square If x2 + bx + c is a perfect square, then it will easily factor to: Ex: Prove the following is a perfect square. Half of b=+8 is +4

8. Completing the Square to Solve a Quadratic Solve the following equation by completing the square: Find the “c” that completes the square GOAL ( x – # )2 = # Isolate the x terms Add the “c” to both sides Factor and Simplify Solve

9. Completing the Square to Solve a Quadratic Solve the following equation by completing the square: Find the “c” that completes the square GOAL ( x – # )2 = # Isolate the x terms Add the “c” to both sides Factor and Simplify Solve