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Solve for aa.\newline −9+7a= 6a\sqrt{\,-9 + 7a} = \sqrt{\,6a}\newlinea= _____a = \,\_\_\_\_\_

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Full solution

Q. Solve for aa.\newline −9+7a= 6a\sqrt{\,-9 + 7a} = \sqrt{\,6a}\newlinea= _____a = \,\_\_\_\_\_
  1. Square Both Sides: Square both sides of the equation to eliminate the square roots.\newline(−9+7a)2=(6a)2(\sqrt{-9 + 7a})^2 = (\sqrt{6a})^2\newline−9+7a=6a-9 + 7a = 6a
  2. Subtract to Isolate 'a': Subtract 6a6a from both sides to get all the terms with 'a' on one side.\newline7a−6a=97a - 6a = 9\newlinea=9a = 9
  3. Check Solution: Check the solution by substituting aa back into the original equation to ensure both sides are equal.(–9+7×9)=(6×9)\sqrt{(–9 + 7\times9)} = \sqrt{(6\times9)}(–9+63)=(54)\sqrt{(–9 + 63)} = \sqrt{(54)}(54)=(54)\sqrt{(54)} = \sqrt{(54)}Both sides are equal, so the solution is correct.

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