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Solve by completing the square.\newlinek2−4k=5k^2 - 4k = 5\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.\newlinek2−4k=5k^2 - 4k = 5\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. Move Constant Term: Write the equation in the form of completing the square.\newlineTo complete the square, the equation must be in the form (k−p)2=q(k - p)^2 = q, where pp and qq are constants. We start by moving the constant term to the right side of the equation.\newlinek2−4k+___=5+___k^2 − 4k + \_\_\_ = 5 + \_\_\_
  2. Find Completion Value: Find the value to complete the square.\newlineTo complete the square, we need to add (42)2=4(\frac{4}{2})^2 = 4 to both sides of the equation.\newlinek2−4k+4=5+4k^2 − 4k + 4 = 5 + 4
  3. Write as Perfect Square: Write the left side of the equation as a perfect square.\newlineNow that we have added 44 to both sides, the left side of the equation is a perfect square.\newline(k−2)2=9(k - 2)^2 = 9
  4. Solve for kk: Solve for kk by taking the square root of both sides.\newlineTo find the value of kk, we take the square root of both sides of the equation.\newlinek−2=±9k - 2 = \pm\sqrt{9}
  5. Positive Square Root: Solve for the positive square root.\newlinek−2=9k - 2 = \sqrt{9}\newlinek−2=3k - 2 = 3\newlinek=3+2k = 3 + 2\newlinek=5k = 5
  6. Negative Square Root: Solve for the negative square root.\newlinek−2=−9k - 2 = -\sqrt{9}\newlinek−2=−3k - 2 = -3\newlinek=−3+2k = -3 + 2\newlinek=−1k = -1

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