9514 1404 393
Answer:
c. {-4}; -8 is extraneous
Explanation:
You might ordinarily solve an equation like this by adding 7, squaring both sides, and solving the resulting quadratic. It would have roots -4 and -8, which you can tell by looking at the answer choices.
You would determine which is extraneous by trying these values in the original equation to see which will satisfy the equation.
Alternatively, you can examine the equation for possible restrictions on the domain. We know the radical cannot be negative, so this becomes ...
(some non-negative number) - 7 = x
That is, x > -7. This means the "solution" x = -8 is extraneous.
{-4}; -8 is extraneous
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Additional comment
I find it often works well to rewrite the equation to the form f(x) = 0 when using a graphing calculator to find the solutions. This can be done by subtracting the right-side expression from both sides of the equation:
√(2x+17) -7 -x = 0
Then the x-intercepts of the graph of the left-side expression are the solutions to the original equation. When square roots (or other even roots) are involved, extraneous solutions will require the negative root be used to make the equation true. The negative branch of the square root is shown on the graph as a dashed line. That branch has an x-intercept of -8, the location of the extraneous solution.