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5.7 – Completing the Square

5.7 – Completing the Square. Completing the square Easy case x² + 8x – 5 = 9. 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. x² + 8x – 5 = 9 x² + 8x = 14 x² + 8x + 16 = 14 + 16 (x+4)² = 30

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5.7 – Completing the Square

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  1. 5.7 – Completing the Square

  2. Completing the squareEasy case x² + 8x – 5 = 9 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 • x² + 8x – 5 = 9 • x² + 8x = 14 • x² + 8x + 16 = 14 + 16 • (x+4)² = 30 • (x+4) = ±√30 • x = -4 ±√30

  3. Completing the squareMedium case 2x² + 12x – 1 = 20 a must be =1. Divide everything by a if it is not already = 1 Add 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

  4. Hard case2x² + 9x = 16 Add 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

  5. WHEW!

  6. Try these on your own: a) x2 -12x +5 =0 b) x2 +8x +36 =0

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