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Solve by completing the square.\newlinef2+20f−17=0f^2 + 20f - 17 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinef=f = _____ or f=f = _____

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Q. Solve by completing the square.\newlinef2+20f−17=0f^2 + 20f - 17 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinef=f = _____ or f=f = _____
  1. Rewrite Equation: Rewrite the equation in the form of f2+bf=cf^2 + bf = c. Add 1717 to both sides to isolate the f2f^2 and ff terms. f2+20f−17+17=0+17f^2 + 20f - 17 + 17 = 0 + 17 f2+20f=17f^2 + 20f = 17
  2. Complete the Square: Choose the number to add to both sides to complete the square.\newlineSince (20/2)2=100(20/2)^2 = 100, add 100100 to both sides.\newlinef2+20f+100=17+100f^2 + 20f + 100 = 17 + 100\newlinef2+20f+100=117f^2 + 20f + 100 = 117
  3. Factor Left Side: Factor the left side of the equation.\newlinef2+20f+100=117f^2 + 20f + 100 = 117\newline(f+10)2=117(f + 10)^2 = 117
  4. Take Square Root: Take the square root of both sides of the equation.\newline(f+10)2=±117\sqrt{(f + 10)^2} = \pm\sqrt{117}\newlinef+10=±117f + 10 = \pm\sqrt{117}
  5. Isolate Variable: Isolate the variable ff by subtracting 1010 from both sides.\newlinef+10−10=±117−10f + 10 - 10 = \pm\sqrt{117} - 10\newlinef=−10±117f = -10 \pm \sqrt{117}
  6. Calculate Decimal Values: Calculate the approximate decimal values of ff.f≈−10±117f \approx -10 \pm \sqrt{117}f≈−10±10.82f \approx -10 \pm 10.82 (rounded to the nearest hundredth)
  7. Find Values of f: Find the two values of f.\newlinef≈−10+10.82f \approx -10 + 10.82 implies f≈0.82f \approx 0.82.\newlinef≈−10−10.82f \approx -10 - 10.82 implies f≈−20.82f \approx -20.82.\newlineValues of f: 0.820.82, −20.82-20.82

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