Notes 9.5 algN (complete square).notebook
February 01, 2016
Notes Section 9.5 ‐ Solving quadratic equations by completing the square
In section 9.3 and 9.4, we solved quations by suare There are 5 ways to solve quadratic equations:
roots and factoring. These methods work in most 1. Graphing
2. Square roots
cases, but not all.
3.
4.
5.
Factoring
Completing the square
Quadratic Formula
If you can change the expression x2 + bx into a perfect‐square trinomial by adding (b/2)2 to x2 + bx = ± c both sides, then you can solve the equation by completing the square. The process is the same whether b is positive or negative.
1. What is the value of c if x2 ‐ 16x + c ?
2. What is the value of c if x2 ‐ 5x + c ?
Find the solution by completing the square.
4. t2 ‐ 8t = 65
3. x2 + 6x = 216
5. x2 ‐ 14x + 16 = 0
6. 2n2 ‐ 6n = 8
7. x2 + 7x ‐ 18 = 0
8. 3x2 ‐ 18x + 9 = 0
9. 4d2 ‐ 12d + 3 = 0