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Solve by completing the square.\newliney2−16y−33=0y^2 - 16y - 33 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____

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Q. Solve by completing the square.\newliney2−16y−33=0y^2 - 16y - 33 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____
  1. Rewrite equation in standard form: Rewrite the equation in the form of y2+by=cy^2 + by = c. Add 3333 to both sides to set the equation up for completing the square. y2−16y−33+33=0+33y^2 - 16y - 33 + 33 = 0 + 33 y2−16y=33y^2 - 16y = 33
  2. Complete the square: Choose the number to add to both sides to complete the square.\newlineSince (−162)2=64(-\frac{16}{2})^2 = 64, add 6464 to both sides.\newliney2−16y+64=33+64y^2 − 16y + 64 = 33 + 64\newliney2−16y+64=97y^2 − 16y + 64 = 97
  3. Factor left side: Factor the left side of the equation.\newliney2−16y+64=97y^2 - 16y + 64 = 97\newline(y−8)2=97(y - 8)^2 = 97
  4. Take square root: Take the square root of both sides of the equation.\newline(y−8)2=97\sqrt{(y − 8)^2} = \sqrt{97}\newliney−8=±97y − 8 = \pm\sqrt{97}
  5. Solve for y: Solve for y by adding 88 to both sides of the equation.\newliney−8+8=±97+8y - 8 + 8 = \pm\sqrt{97} + 8\newliney=8±97y = 8 \pm \sqrt{97}
  6. Calculate decimal values: Calculate the approximate decimal values of yy, rounded to the nearest hundredth.y≈8+97y \approx 8 + \sqrt{97} implies y≈8+9.85y \approx 8 + 9.85 which is y≈17.85y \approx 17.85.y≈8−97y \approx 8 - \sqrt{97} implies y≈8−9.85y \approx 8 - 9.85 which is y≈−1.85y \approx -1.85.Values of yy: 17.8517.85, −1.85-1.85

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