y=-100x-((x^2)/2)

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Solution for y=-100x-((x^2)/2) equation: 


x in (-oo:+oo)

y = -((x^2)/2)-100*x // + -((x^2)/2)-100*x

(x^2)/2-(-100*x)+y = 0

(x^2)/2+100*x+y = 0

1/2*x^2+100*x+y = 0

DELTA = 100^2-(1/2*4*y)

DELTA = 10000-2*y

10000-2*y = 0

10000-2*y = 0 // - 10000

-2*y = -10000 // : -2

y = -10000/(-2)

y = 5000

DELTA = 0  <=>  t_1 = 5000

x = -100/(1/2*2) i y = 5000

x = -100 i y = 5000

( x = ((10000-2*y)^(1/2)-100)/(1/2*2) or x = (-(10000-2*y)^(1/2)-100)/(1/2*2) ) i y > 5000

( x = (10000-2*y)^(1/2)-100 or x = -((10000-2*y)^(1/2)+100) ) i y > 5000

y-5000 > 0

y-5000 > 0 // + 5000

y > 5000

x in { -100, (10000-2*y)^(1/2)-100, -((10000-2*y)^(1/2)+100) }

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