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Solve by completing the square.\newlinek2−18k−41=0k^2 - 18k - 41 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____

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Q. Solve by completing the square.\newlinek2−18k−41=0k^2 - 18k - 41 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____
  1. Rewrite and Add 4141: Rewrite the equation in the form of k2+bk=ck^2 + bk = c. Add 4141 to both sides to set the equation up for completing the square. k2−18k−41+41=0+41k^2 - 18k - 41 + 41 = 0 + 41 k2−18k=41k^2 - 18k = 41
  2. Choose Number to Add: Choose the number to add to both sides to complete the square.\newlineSince (−182)2=81(-\frac{18}{2})^2 = 81, add 8181 to both sides.\newlinek2−18k+81=41+81k^2 − 18k + 81 = 41 + 81\newlinek2−18k+81=122k^2 − 18k + 81 = 122
  3. Factor Left Side: Factor the left side of the equation.\newlinek2−18k+81=122k^2 - 18k + 81 = 122\newline(k−9)2=122(k - 9)^2 = 122
  4. Take Square Root: Take the square root of both sides of the equation.\newline(k−9)2=±122\sqrt{(k − 9)^2} = \pm\sqrt{122}\newlinek−9=±122k − 9 = \pm\sqrt{122}
  5. Solve for kk: Solve for kk by adding 99 to both sides of the equation.\newlinek−9+9=±122+9k - 9 + 9 = \pm\sqrt{122} + 9\newlinek=9±122k = 9 \pm \sqrt{122}
  6. Calculate Approximate Values: Calculate the approximate values of kk, rounding to the nearest hundredth.k≈9+122k \approx 9 + \sqrt{122} or k≈9−122k \approx 9 - \sqrt{122}k≈9+11.05k \approx 9 + 11.05 or k≈9−11.05k \approx 9 - 11.05k≈20.05k \approx 20.05 or k≈−2.05k \approx -2.05

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