Question 206050
Is the equation {{{(q+5)/q=-6}}} ???



{{{(q+5)/q=-6}}} Start with the given equation.



{{{q+5=-6q}}} Multiply both sides by 'q'.



{{{q=-6q-5}}} Subtract {{{5}}} from both sides.



{{{q+6q=-5}}} Add {{{6q}}} to both sides.



{{{7q=-5}}} Combine like terms on the left side.



{{{q=(-5)/(7)}}} Divide both sides by {{{7}}} to isolate {{{q}}}.



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Answer:


So the solution is {{{q=-5/7}}} which approximates to {{{q=-0.714}}}. 



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OR...Is the equation {{{q+5/q=-6}}} ???



{{{q+5/q=-6}}} Start with the given equation.



{{{q^2+5=-6q}}} Multiply EVERY term by the LCD 'q' to clear out the fractions.



{{{q^2+6q+5=0}}} Add 6q to both sides.



Notice that the quadratic {{{q^2+6q+5}}} is in the form of {{{Aq^2+Bq+C}}} where {{{A=1}}}, {{{B=6}}}, and {{{C=5}}}



Let's use the quadratic formula to solve for "q":



{{{q = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{q = (-(6) +- sqrt( (6)^2-4(1)(5) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=6}}}, and {{{C=5}}}



{{{q = (-6 +- sqrt( 36-4(1)(5) ))/(2(1))}}} Square {{{6}}} to get {{{36}}}. 



{{{q = (-6 +- sqrt( 36-20 ))/(2(1))}}} Multiply {{{4(1)(5)}}} to get {{{20}}}



{{{q = (-6 +- sqrt( 16 ))/(2(1))}}} Subtract {{{20}}} from {{{36}}} to get {{{16}}}



{{{q = (-6 +- sqrt( 16 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{q = (-6 +- 4)/(2)}}} Take the square root of {{{16}}} to get {{{4}}}. 



{{{q = (-6 + 4)/(2)}}} or {{{q = (-6 - 4)/(2)}}} Break up the expression. 



{{{q = (-2)/(2)}}} or {{{q =  (-10)/(2)}}} Combine like terms. 



{{{q = -1}}} or {{{q = -5}}} Simplify. 



So the solutions are {{{q = -1}}} or {{{q = -5}}}