<PRE><B>Question 130951</B>
{{{x^2+5x-3=0}}}


Completing the square is inconvenient because the coefficient on the x term is odd, so just use the quadratic formula:


{{{x = (-red(b) +- sqrt( red(b)^2-4*green(a)*blue(c) ))/(2*green(a)) }}}


{{{x = (-red(5) +- sqrt( red(5)^2-4*green(1)*blue((-3)) ))/(2*green(1)) }}}  


{{{x = (-5 +- sqrt( 25+12 ))/2 }}}


{{{x = (-5 +- sqrt( 37 ))/2 }}}


37 is prime so there is no further simplification possible, and the two values presented above are the exact roots of the equation.  As to the 3-decimal place accurate approximation, you can push calculator buttons as well as I can.


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