Question

watch the video and then solve the problem given below
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solve the radical equation check all proposed solutions
\\(\sqrt{2x + 1}+7 = x\\)

select the correct choice below and, if necessary, fill in the answer box to complete your choice
\\(\bigcirc\\) a. the solution set is \\(\\{\\}\\).
(use a comma to separate answers as needed simplify your answer.)
\\(\bigcirc\\) b. the solution set is \\(\varnothing\\).

Explanation:

Step1: Isolate the radical term

Subtract 7 from both sides to get the square root alone.
$\sqrt{2x+1} = x - 7$

Step2: Square both sides

Eliminate the square root by squaring each side.
$(\sqrt{2x+1})^2 = (x - 7)^2$
$2x + 1 = x^2 - 14x + 49$

Step3: Rearrange to quadratic form

Move all terms to one side to set equation to 0.
$x^2 - 16x + 48 = 0$

Step4: Factor the quadratic

Find two factors of 48 that add to -16.
$(x - 12)(x - 4) = 0$

Step5: Solve for x

Set each factor equal to 0 and solve.
$x - 12 = 0 \implies x=12$; $x - 4 = 0 \implies x=4$

Step6: Check solutions

Substitute back into original equation to verify.
For $x=12$: $\sqrt{2(12)+1} +7 = \sqrt{25}+7=5+7=12$, which equals x. Valid.
For $x=4$: $\sqrt{2(4)+1} +7 = \sqrt{9}+7=3+7=10
eq 4$. Invalid.

Answer:

A. The solution set is {12}