Question

solve the equation.$x - \sqrt{8 - 2x} = 0$select the correct choice below and, if necessary, fill in the answer box to complete your choice.a. the solution set is {}.(simplify your answer. use a comma to separate answers as needed.)b. there is no solution.

Explanation:

Step1: Isolate the radical term

$x = \sqrt{8 - 2x}$

Step2: Square both sides to eliminate radical

$x^2 = (\sqrt{8 - 2x})^2$
$x^2 = 8 - 2x$

Step3: Rearrange to quadratic equation

$x^2 + 2x - 8 = 0$

Step4: Factor the quadratic

$(x + 4)(x - 2) = 0$

Step5: Solve for x values

$x + 4 = 0 \implies x = -4$
$x - 2 = 0 \implies x = 2$

Step6: Verify solutions in original equation

For $x=-4$: $-4 - \sqrt{8 - 2(-4)} = -4 - \sqrt{16} = -4 - 4 = -8
eq 0$ (invalid)
For $x=2$: $2 - \sqrt{8 - 2(2)} = 2 - \sqrt{4} = 2 - 2 = 0$ (valid)

Answer:

A. The solution set is {2}.