Question 120366
If {{{3+2i}}} is a solution, this means {{{x=3+2i}}}




{{{x=3+2i}}} Start with the given equation




{{{x-3=2i}}} Subtract 3 from both sides



{{{(x-3)/2=i}}} Divide both sides by 2 to isolate "i"



{{{(x-3)/2=sqrt(-1)}}} Replace i with {{{sqrt(-1)}}}. Remember {{{i=sqrt(-1)}}}



{{{((x-3)/2)^2=-1}}} Square both sides




{{{(x-3)^2/2^2=-1}}} Distribute the exponent




{{{(x-3)^2/4=-1}}} Square 2 to get 4




{{{(1/4)(x-3)^2=-1}}} Rearrange the terms



{{{(1/4)(x-3)^2+1=0}}} Add 1 to both sides




{{{(1/4)(x^2-6x+9)+1=0}}} Foil



{{{(1/4)x^2-(3/2)x+9/4+1=0}}} Distribute



{{{(1/4)x^2-(3/2)x+13/4=0}}} Combine like terms




{{{4((1/4)x^2-(3/2)x+13/4)=0}}} Multiply both sides by the LCD 4 to eliminate any fractions



{{{x^2-6x+13=0}}} Distribute. Notice how the fractions have been eliminated.




So the quadratic that has the solution {{{3+2i}}} is {{{y=x^2-6x+13}}}



Since m is the coefficient for the x term in {{{x^2+mx+n=0}}}, this means {{{mx=-6x}}} and that {{{m=-6}}}



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Answer: 


So the value of m is {{{m=-6}}}





Check:


You can check your answer by using the quadratic formula