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Solve by completing the square.\newlinek2−14k−5=0k^2 - 14k - 5 = 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.\newlinek2−14k−5=0k^2 - 14k - 5 = 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 that separates the constant term from the k terms.\newlinek2−14k=5k^2 - 14k = 5
  2. Find Completes Square: Find the number that completes the square for the kk terms. This is done by taking half of the coefficient of kk and squaring it.(−142)2=49(−\frac{14}{2})^2 = 49
  3. Add/Subtract to Complete Square: Add and subtract this number to the left side of the equation to complete the square, and add it to the right side to keep the equation balanced.\newlinek2−14k+49=5+49k^2 - 14k + 49 = 5 + 49
  4. Write as Squared Binomial: Write the left side of the equation as a squared binomial and simplify the right side.\newline(k−7)2=54(k - 7)^2 = 54
  5. Take Square Root: Take the square root of both sides of the equation to solve for kk.k−7=±54k - 7 = \pm\sqrt{54}
  6. Simplify Square Root: Simplify the square root of 5454. Since 54=9×654 = 9 \times 6 and the square root of 99 is 33, we can write 54\sqrt{54} as 363\sqrt{6}. \newlinek−7=±36k - 7 = \pm3\sqrt{6}
  7. Solve for k: Solve for k by adding 77 to both sides of the equation.k=7±36k = 7 \pm 3\sqrt{6}
  8. Approximate Square Root: Since the question asks for the answer as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth, we need to approximate 363\sqrt{6}. \newline36≈3×2.45≈7.353\sqrt{6} \approx 3 \times 2.45 \approx 7.35
  9. Write Approximate Values: Now, write the approximate values of kk to the nearest hundredth.k≈7+7.35k \approx 7 + 7.35 or k≈7−7.35k \approx 7 - 7.35k≈14.35k \approx 14.35 or k≈−0.35k \approx -0.35

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