Question 196523
{{{sqrt(2n-8)=-3}}} Start with the given equation.



{{{(sqrt(2n-8))^2=(-3)^2}}} Square both sides



{{{2n-8=(-3)^2}}} Square the square root to eliminate it



{{{2n-8=9}}} Square -3 to get 9 (NOT -9). Note: this is where you made a mistake



{{{2n=9+8}}} Add {{{8}}} to both sides.



{{{2n=17}}} Combine like terms on the right side.



{{{n=(17)/(2)}}} Divide both sides by {{{2}}} to isolate {{{n}}}.





So the <i>possible</i> solution is {{{n=17/2}}}.



However, we need to check the possible solution.



Check:



{{{sqrt(2n-8)=-3}}} Start with the given equation.



{{{sqrt(2(17/2)-8)=-3}}} Plug in {{{n=17/2}}}



{{{sqrt(34/2-8)=-3}}} Multiply



{{{sqrt(17-8)=-3}}} Reduce



{{{sqrt(9)=-3}}} Subtract



{{{3=-3}}} Take the square root of 9 to get 3



Since the both sides are clearly NOT equal, this means that {{{n=17/2}}} is NOT a solution.



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Answer:



So there are no solutions.



Note: an extraneous solution is a "solution" that is introduced in the intermediate steps but does NOT satisfy the original equation (the only equation we care about)