Question 172644


{{{-4(k-8)^2=16}}} Start with the given equation.



{{{(k-8)^2=(16)/(-4)}}} Divide both sides by {{{-4}}}.



{{{(k-8)^2=-4}}} Reduce.



{{{x-8=0+-sqrt(-4)}}} Take the square root of both sides.



{{{k-8=sqrt(-4)}}} or {{{k-8=-sqrt(-4)}}} Break up the "plus/minus" to form two equations.



{{{k-8=2i}}} or {{{k-8=-2i}}}  Simplify the square root. Note: {{{i=sqrt(-1)}}}



{{{k=8+2i}}} or {{{k=8-2i}}} Add {{{8}}} to both sides.




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Answer:



So the solutions are {{{k=8+2i}}} or {{{k=8-2i}}}.