Solve the radical equation, and check all proposed solutions.
-$$x - \sqrt { 3 x - 2 } = 4$$
A) $\{ 9 \}$
B) $\{ 1,2 \}$
C) $\{ - 1 \}$
D) $\{ 2,9 \}$

Question

Quizplus · Accepted Answer

To solve the equation $x - \sqrt{3x - 2} = 4$, first isolate the square root term: $\sqrt{3x - 2} = x - 4$. Squaring both sides gives $3x - 2 = (x - 4)^2$, which simplifies to $3x - 2 = x^2 - 8x + 16$. Rearranging gives $x^2 - 11x + 18 = 0$, which factors to $(x - 9)(x - 2) = 0$. Thus, $x = 9$ or $x = 2$. Checking both solutions in the original equation, only $x = 9$ satisfies it, as $x = 2$ does not.

Solve the Radical Equation, and Check All Proposed Solutions x−3x−2=4x - \sqrt { 3 x - 2 } = 4x−3x−2​=4

Solve the Radical Equation, and Check All Proposed Solutions $x - \sqrt { 3 x - 2 } = 4$