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Solve by completing the square.\newlineq2−24q+41=0q^2 - 24q + 41 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineq=q = _____ or q=q = _____

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Q. Solve by completing the square.\newlineq2−24q+41=0q^2 - 24q + 41 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineq=q = _____ or q=q = _____
  1. Rewrite Equation: Rewrite the equation in the form of q2+bq=cq^2 + bq = c.\newlineSubtract 4141 from both sides to set the equation up for completing the square.\newlineq2−24q+41−41=0−41q^2 - 24q + 41 - 41 = 0 - 41\newlineq2−24q=−41q^2 - 24q = -41
  2. Subtract 4141: Choose the number to add to both sides to complete the square.\newlineSince (−24/2)2=144(-24/2)^2 = 144, add 144144 to both sides.\newlineq2−24q+144=−41+144q^2 − 24q + 144 = -41 + 144\newlineq2−24q+144=103q^2 − 24q + 144 = 103
  3. Choose Number to Add: Factor the left side of the equation.\newlineq2−24q+144=103q^2 - 24q + 144 = 103\newline(q−12)2=103(q - 12)^2 = 103
  4. Factor Left Side: Take the square root of both sides of the equation.\newline(q−12)2=103\sqrt{(q - 12)^2} = \sqrt{103}\newlineq−12=±103q - 12 = \pm\sqrt{103}
  5. Take Square Root: Solve for qq by adding 1212 to both sides of the equation.\newlineq−12+12=±103+12q - 12 + 12 = \pm\sqrt{103} + 12\newlineq=12±103q = 12 \pm \sqrt{103}
  6. Solve for q: Calculate the approximate decimal values of q, rounded to the nearest hundredth. \newlineq≈12+103q \approx 12 + \sqrt{103} or q≈12−103q \approx 12 - \sqrt{103}\newlineq≈12+10.15q \approx 12 + 10.15 or q≈12−10.15q \approx 12 - 10.15\newlineq≈22.15q \approx 22.15 or q≈1.85q \approx 1.85

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