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Solve for kk.\newline6+3k=6k\sqrt{6 + 3k} = \sqrt{6k}\newlinek=k = _____

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Full solution

Q. Solve for kk.\newline6+3k=6k\sqrt{6 + 3k} = \sqrt{6k}\newlinek=k = _____
  1. Square both sides: Square both sides of the equation to eliminate the square roots.\newline(6+3k)2=(6k)2(\sqrt{6 + 3k})^2 = (\sqrt{6k})^2\newline6+3k=6k6 + 3k = 6k
  2. Subtract 66: Subtract 66 from both sides to get the terms with kk on one side and constants on the other.\newline6+3k−6=6k−66 + 3k - 6 = 6k - 6\newline3k=6k−63k = 6k - 6
  3. Isolate kk terms: Subtract 6k6k from both sides to isolate the kk terms on one side.\newline3k−6k=6k−6k−63k - 6k = 6k - 6k - 6\newline−3k=−6-3k = -6
  4. Divide by −3-3: Divide both sides by −3-3 to solve for kk.\newline−3k−3=−6−3\frac{-3k}{-3} = \frac{-6}{-3}\newlinek=2k = 2

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