Question 67112
The given equation is: 


{{{x^2 + 2x + 5 = 0}}}  


The last constant term is 5, this can be factored as 5 * 1 


Neither addtion of these two factors nor the subtraction gives us the middle term +2. 


Hence, to find the roots of the equation, we use the quadratic formula. This is given by: 


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


From the given equation, we find the values of a, b and c from the given equation.


Hence, a = 1, b = 2 and c = 5. Substitute these values in the above formula.



{{{x = (-2 +- sqrt( 2^2-4*1*5 ))/(2*1) }}}



{{{x = (-2 +- sqrt( 4-20 ))/(2)}}} 


{{{x = (-2 +- sqrt(-16))/2}}} 


{{{x = (-2 +- 4i)/2}}} 


{{{x = -1 + - 2i}}} 


Hence, the answer.


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