What is two numbers that when added equal 25 but when multiplied equal negative 200

Well lets look at it lets find multiples that equal 200 when multiplied first to get rid of extra work 

so i just took a couple of guesses and lined them up 
i got really close when i did this one 
-200/30 = -6.666666667
30 + 6.666666667 = 23.33333333
see not quite there almost 25 but not far enough 
so ill try to move the numbers around little by little. 
-200/29.5 = -6.779661017
29.5 + -6.779661017 = 22.72033898
okay honestly after i finished this trial i wasn't sure if i was thinking straight because i completely didnt think about which way i needed to go so now i pinched myself and this time we might head the right way lol
-200/30.5 = -6.557377049
30.5 + -6.557377049 = 23.94262295
so obviously we need to move up alittle more 
-200/31 = -6.451612903
31 + -6.451612903 = 24.5483871
HEY LOOK WE ARE ALMOST THERE!! lets try some more;)
-200/31.5 = -6.349206349
31.5 + -6.349206349 = 25.15079365
see we are at 25! but lets try to get rid of as many numbers behind it as possible.
-200/31.4 = -6.369426752
31.4 + -6.369426752 = 25.03057325
getting closer...
-200/31.39 = -6.371455878
31.39 + -6.371455878 = 25.01854412
what does this mean? this means we can go lower... sooo here we go 
-200/31.38 = -6.373486297
31.38 + -6.373486297 = 25.0065137
i guess we can try lower..
-200/31.37 = -6.375518011
31.37 + -6.375518011 = 24.99448199
wait! before you leave! try 31.379
-200/31.379 = -6.37368941
31.379 + -6.37368941 = 25.00531059
okay so yes, i am taking the very long way but good comes to those with patience:D lets try making the third place after the decimal a little bit lower
-200/31.377 = -6.374095675
31.377 + -6.374095675 = 25.00290432
yes we can take it lower so lets make it the best answer 
-200/31.376 = -6.374298827
31.376 + -6.374298827 = 25.00170117
i pray this be over soon^ lets try again
-200/31.375 = -6.374501992
31.375 + -6.374501992 = 25.00049801
okay im a perfectionist... sooo lets go lower
-200/31.374 = -6.37470517
31.374 + -6.37470517 = 24.99929483
okay so we went to low on the third place. and of course i am moving to the fourth place...
-200/31.3749 = -6.374522309
31.3749 + -6.374522309 = 25.00037769
okay we can move lower on that place
-200/31.3748 = -6.374542627
31.3748 + -6.374542627 = 25.00025737
lets try to move this along faster...
-200/31.3746 = -6.374583262
31.3746 + -6.374583262 = 25.00001674 
every number counts literally so moving lower 
-200/31.3744 = -6374623897
31.3744 + -6374623897 = 24.9997761 
we gotta put a 9 on our fifth place from our decimal sooo here we go again
-200/31.37449 = -6.374605611
31.37449 + -6.374605611 = 24.9998439
OMG DO YOU UNDERSTAND WHAT THIS MEANS!!?!?!
okay that means our answer was two trials ago solved 
in other words our two numbers arreee
 31.3746
-6.374583262
hallelujah we are finished and if this is wrong i will pull my hair out.