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Solve by completing the square.\newlinek2+6k=23k^2 + 6k = 23\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+6k=23k^2 + 6k = 23\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 Equation: Rewrite the equation in the form of x2+bx=cx^2 + bx = c.\newlinek2+6k=23k^2 + 6k = 23
  2. Complete the Square: Choose the number to add to both sides to complete the square.\newlineSince (62)2=9(\frac{6}{2})^2 = 9, add 99 to both sides.\newlinek2+6k+9=23+9k^2 + 6k + 9 = 23 + 9\newlinek2+6k+9=32k^2 + 6k + 9 = 32
  3. Factor Left Side: Identify the equation after factoring the left side.\newlinek2+6k+9=32k^2 + 6k + 9 = 32\newline(k+3)2=32(k + 3)^2 = 32
  4. Take Square Root: Identify the equation after taking the square root on both sides.\newlineTake the square root of both sides of the equation.\newline(k+3)2=32\sqrt{(k + 3)^2} = \sqrt{32}\newlinek+3=±32k + 3 = \pm\sqrt{32}
  5. Simplify Square Root: Simplify the square root and round the non-terminating values to the nearest hundredth. \newlinek+3=±32k + 3 = \pm\sqrt{32}\newlinek+3=±5.66k + 3 = \pm5.66 (rounded to the nearest hundredth)
  6. Isolate Variable: Choose the equation after isolating the variable kk. To isolate kk, subtract 33 from both sides of the equation. k+3−3=±5.66−3k + 3 - 3 = \pm 5.66 - 3 k=2.66k = 2.66 or k=−8.66k = -8.66 (rounded to the nearest hundredth)

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