Solve the following equations. (a) sqrt(3x-5)+3=x

Isolate Square Root: Isolate the square root on one side of the equation. sqrt(3x-5) = x - 3Square Both Sides: Square both sides to eliminate the square root. (sqrt(3x-5))^2 = (x - 3)^2 3x - 5 = (x - 3)(x - 3)Expand Equation: Expand the right side of the equation. 3x - 5 = x^2 - 6x + 9Combine Like Terms: Move all terms to one side to set the equation to zero and combine like terms. 0 = x^2 - 6x - 3x + 9 + 5 0 = x^2 - 9x + 14Factor Quadratic Equation: Factor the quadratic equation. 0 = (x - 7)(x - 2)Solve for x: Set each factor equal to zero and solve for x. x - 7 = 0 or x - 2 = 0 x = 7 or x = 2Check Solutions: Check both solutions in the original equation to ensure they do not result in taking the square root of a negative number or any other invalid operation. For x = 7: sqrt(3*7 - 5) + 3 = 7 sqrt(21 - 5) + 3 = 7 sqrt(16) + 3 = 7 4 + 3 = 7 7 = 7 (Valid solution)For x = 2: sqrt(3*2 - 5) + 3 = 2 sqrt(6 - 5) + 3 = 2 sqrt(1) + 3 = 2 1 + 3 = 2 4 ≠ 2 (Invalid solution)

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Solve the following equations.
(a)
sqrt(3x-5)+3=x

Solve the following equations. $\newline$ (a) $\sqrt{3 x-5}+3=x$

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Q. Solve the following equations.

\newline

(a)

\sqrt{3 x-5}+3=x

Isolate Square Root: Isolate the square root on one side of the equation. $\sqrt{3x-5} = x - 3$
Square Both Sides: Square both sides to eliminate the square root. $\newline$ $(\sqrt{3x-5})^2 = (x - 3)^2$ $\newline$ $3x - 5 = (x - 3)(x - 3)$
Expand Equation: Expand the right side of the equation. $3x - 5 = x^2 - 6x + 9$
Combine Like Terms: Move all terms to one side to set the equation to zero and combine like terms. $\newline$ $0 = x^2 - 6x - 3x + 9 + 5$ $\newline$ $0 = x^2 - 9x + 14$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $0 = (x - 7)(x - 2)$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $x - 7 = 0$ or $x - 2 = 0$ $\newline$ $x = 7$ or $x = 2$
Check Solutions: Check both solutions in the original equation to ensure they do not result in taking the square root of a negative number or any other invalid operation. $\newline$ For $x = 7$ : $\newline$ $\sqrt{3\times7 - 5} + 3 = 7$ $\newline$ $\sqrt{21 - 5} + 3 = 7$ $\newline$ $\sqrt{16} + 3 = 7$ $\newline$ $4 + 3 = 7$ $\newline$ $7 = 7$ (Valid solution)
Check Solutions: Check both solutions in the original equation to ensure they do not result in taking the square root of a negative number or any other invalid operation. $\newline$ For $x = 7$ : $\newline$ $\sqrt{3\times7 - 5} + 3 = 7$ $\newline$ $\sqrt{21 - 5} + 3 = 7$ $\newline$ $\sqrt{16} + 3 = 7$ $\newline$ $4 + 3 = 7$ $\newline$ $7 = 7$ (Valid solution)For $x = 2$ : $\newline$ $\sqrt{3\times2 - 5} + 3 = 2$ $\newline$ $\sqrt{6 - 5} + 3 = 2$ $\newline$ $\sqrt{1} + 3 = 2$ $\newline$ $\sqrt{3\times7 - 5} + 3 = 7$ $0$ $\newline$ $\sqrt{3\times7 - 5} + 3 = 7$ $1$ (Invalid solution)