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Solve by completing the square.\newlinef2−20f=41f^2 - 20f = 41\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=41f^2 - 20f = 41\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 and Subtract: Rewrite the equation in the form of f2+bf=cf^2 + bf = c.\newlineSubtract 4141 from both sides to set the equation to zero.\newlinef2−20f−41=0f^2 - 20f - 41 = 0
  2. Complete the Square: Choose the equation after completing the square.\newlineSince (−202)2=100(-\frac{20}{2})^2 = 100, add 100100 to both sides to complete the square.\newlinef2−20f+100=41+100f^2 - 20f + 100 = 41 + 100\newlinef2−20f+100=141f^2 - 20f + 100 = 141
  3. Factor and Identify: Identify the equation after factoring the left side.\newlinef2−20f+100=141f^2 - 20f + 100 = 141\newline(f−10)2=141(f - 10)^2 = 141
  4. Take Square Root: Identify the equation after taking the square root on both sides.\newlineTake the square root of both sides of the equation.\newline(f−10)2=141\sqrt{(f - 10)^2} = \sqrt{141}\newlinef−10=±141f - 10 = \pm\sqrt{141}
  5. Isolate Variable: Choose the equation after isolating the variable ff. To isolate ff, add 1010 to both sides of the equation. f−10+10=±141+10f - 10 + 10 = \pm\sqrt{141} + 10 f=10±141f = 10 \pm \sqrt{141}
  6. Calculate Approximate Values: Calculate the approximate values of ff, rounding to the nearest hundredth.f≈10+141f \approx 10 + \sqrt{141} and f≈10−141f \approx 10 - \sqrt{141}f≈10+11.87f \approx 10 + 11.87 and f≈10−11.87f \approx 10 - 11.87f≈21.87f \approx 21.87 and f≈−1.87f \approx -1.87

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