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Solve for uu.\newline5u−8=u\sqrt{5u - 8} = \sqrt{u}\newlineu=u = _____

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Full solution

Q. Solve for uu.\newline5u−8=u\sqrt{5u - 8} = \sqrt{u}\newlineu=u = _____
  1. Square both sides: Square both sides of the equation to eliminate the square roots.\newline(5u−8)2=(u)2(\sqrt{5u − 8})^2 = (\sqrt{u})^2\newline5u−8=u5u − 8 = u
  2. Subtract uu: Subtract uu from both sides to get all the uu terms on one side.\newline5u−u−8=u−u5u − u − 8 = u − u\newline4u−8=04u − 8 = 0
  3. Add 88: Add 88 to both sides to isolate the term with uu.\newline4u−8+8=0+84u - 8 + 8 = 0 + 8\newline4u=84u = 8
  4. Divide by 44: Divide both sides by 44 to solve for uu.4u4=84\frac{4u}{4} = \frac{8}{4}u=2u = 2

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