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Solve for xx.\newline(8x5)=3x\sqrt{(-8x - 5)} = \sqrt{-3x}\newlinex=x = _____

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Q. Solve for xx.\newline(8x5)=3x\sqrt{(-8x - 5)} = \sqrt{-3x}\newlinex=x = _____
  1. Square Both Sides: Square both sides of the equation to eliminate the square roots.\newline(8x5)2=(3x)2(\sqrt{\text{–}8x − 5})^2 = (\sqrt{\text{–}3x})^2\newline8x5=3x\text{–}8x − 5 = \text{–}3x
  2. Move Variable Terms: Move the variable terms to one side of the equation by adding 8x8x to both sides.\newline8x5+8x=3x+8x-8x - 5 + 8x = -3x + 8x\newline5=5x-5 = 5x
  3. Divide Both Sides: Divide both sides by 55 to solve for xx.55=5x5\frac{-5}{5} = \frac{5x}{5}$x=1\$x = -1)
  4. Check Solution: Check the solution by substituting x=1x = -1 back into the original equation.(8(1)5)=(3(1))\sqrt{(-8(-1) - 5)} = \sqrt{(-3(-1))}(85)=(3)\sqrt{(8 - 5)} = \sqrt{(3)}(3)=(3)\sqrt{(3)} = \sqrt{(3)}This confirms that x=1x = -1 is a valid solution.

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