Question 1038841
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Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x. 
(Enter your answers as a comma-separated list. Round each answer to four decimal places.)

tan^2 x + 5 tan x + 3 = 0
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Introduce new variable u = tan(x).
Then your equation becomes

{{{u^2 + 5u + 3}}} = {{{0}}}.

Solve this quadratic equation by quadratic formula. You will get

{{{u[1,2]}}} = {{{(-5 +- sqrt(25-4*3))/2}}} = {{{(-5 +- sqrt(13))/2}}}.

{{{u[1]}}} = {{{(-5+sqrt(13))/2}}}  --->  tan(x) = {{{(-5+sqrt(13))/2}}}  --->  x = {{{arctan((-5+sqrt(13))/2)}}}  --->  apply your calculator.

{{{u[2]}}} = {{{(-5-sqrt(13))/2}}}  --->  tan(x) = {{{(-5-sqrt(13))/2}}}  --->  x = {{{arctan((-5-sqrt(13))/2))}}}  --->  apply your calculator.
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