Question 410826
Not quite. You have a sign error in the following steps:


-10+-sqrt((10)^2-4(5)(22)/2(5)
-10+-sqrt(100-(-440))/(10)   <--- should be 100 - 440, not 100 - (-440). Also, 100 - (-440) = 540, not 500.


By the quadratic formula, {{{x = (-10 +- sqrt(100 - 440))/10 = (-10 +- sqrt(-340))/10}}}. We can factor 4 out of {{{sqrt(-340)}}} to obtain {{{2sqrt(-85)}}}. This becomes


{{{(-10 +- 2sqrt(-85))/10 = (-5 +-sqrt(-85))/5 = (-5 +- i*sqrt(85))/5}}}.


In addition, it is more conventional (and less likely to make a mistake) to write the quadratic as {{{5x^2 + 10x + 22}}} instead of {{{5x^2 + 22 + 10x}}}.