1. 5.7 – Completing the Square

2. Completing the square Easy case x² + 8x – 5 = 9 x² + 8x – 5 = 9 x² + 8x = 14 x² + 8x + 16 = 14 + 16 (x+4)² = 30 (x+4) = ±√30 x = -4 ±√30 Add the numbers to right, variables to the left Add 16 to both sides Factor the left side Square root both sides Get x by itself

3. Completing the square Medium case 2x² + 12x – 1 = 20 2x² + 12x – 1 = 20 2x² + 12x = 21 x² + 6x = 10.5 x² + 6x + 9 = 10.5 + 9 (x+3)² = 19.5 (x+3) = ±√19.5 x = -3 ±√30 Add a must be =1. Divide everything by a if it is not already = 1

4. Hard case 2x² + 9x = 16 2x² + 9x = 16 x² + 9/2 x + 81/16 = 8 + 81/16 (x + 9/4)²= 8 + 81/16 (x + 9/4)²= 128/16 + 81/16 (x + 9/4)²= 209/16 (x + 9/4) = ±√(209/16) (x + 9/4) = ±√209/4 x = -9/4 ± √209/4 Add

5. WHEW!

6. Try these on your own: a)x 2 -12x +5 =0 b) x 2 +8x +36 =0