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Solve by completing the square.\newlinek2−16k+37=0k^2 - 16k + 37 = 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.\newlinek2−16k+37=0k^2 - 16k + 37 = 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. Write Equation Form: Write the equation in the form of k2+bk=ck^2 + bk = c. The given equation is already in this form: k2−16k+37=0k^2 - 16k + 37 = 0.
  2. Move Constant Term: Move the constant term to the other side of the equation.\newlineSubtract 3737 from both sides to isolate the kk terms.\newlinek2−16k=−37k^2 - 16k = -37
  3. Find Completing Square Number: Find the number to complete the square.\newlineTo complete the square, we need to add (b/2)2(b/2)^2 to both sides, where bb is the coefficient of kk. In this case, b=−16b = -16.\newline(−16/2)2=(−8)2=64(-16/2)^2 = (-8)^2 = 64\newlineAdd 6464 to both sides of the equation.\newlinek2−16k+64=−37+64k^2 − 16k + 64 = -37 + 64
  4. Write Left Side Perfect Square: Write the left side as a perfect square and simplify the right side.\newlinek2−16k+64=27k^2 - 16k + 64 = 27\newline(k−8)2=27(k - 8)^2 = 27
  5. Take Square Root: Take the square root of both sides of the equation.\newline(k−8)2=±27\sqrt{(k - 8)^2} = \pm\sqrt{27}\newlinek−8=±27k - 8 = \pm\sqrt{27}
  6. Solve for kk: Solve for kk by isolating the variable.\newlineAdd 88 to both sides of the equation.\newlinek=8±27k = 8 \pm \sqrt{27}
  7. Simplify Square Root: Simplify the square root and round to the nearest hundredth if necessary.\newline27≈5.20\sqrt{27} \approx 5.20 (rounded to the nearest hundredth)\newlinek≈8±5.20k \approx 8 \pm 5.20
  8. Find Two Values of kk: Find the two values of kk. k≈8+5.20k \approx 8 + 5.20 implies k≈13.20k \approx 13.20. k≈8−5.20k \approx 8 - 5.20 implies k≈2.80k \approx 2.80. Values of kk: 13.2013.20, 2.802.80

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