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Answer 1 · 2018-02-14T03:13:19

The exact answer is $x=(tan^-1(-14)-5)/4+(pik)/4$

which is about $-1.6249+(pik)/4$ .

Simply take the inverse tangent of both sides:

$color(white)(=>)tan(4x+5)=-14$

$=>color(red)(cancel(color(black)(tan^-1)))(color(red)(cancel(color(black)tan))(4x+5))=tan^-1(-14)$

$color(white)(=>)4x+5=tan^-1(-14)$

$color(white)(=>)4x=tan^-1(-14)-5$

$color(white)(=>)x=(tan^-1(-14)-5)/4$

$color(white)(=>x)~~-1.6249...$

Now, since the period of the $tan(4x+5)$ is $pi/4$ , that means the answer is correct every $pi/4$ , so we need to add that as a constant:

$x=(tan^-1(-14)-5)/4+(pik)/4$

where $k$ is any integer.