-1/2(x+1)^2+1

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Solution for -1/2(x+1)^2+1 equation: 


x in (-oo:+oo)

(-1/2)*(x+1)^2+1 = 0

1-1/2*(x+1)^2 = 0

1-1/2*(x+1)^2 = 0

1/2-1/2*x^2-x = 0

1/2-1/2*x^2-x = 0

1/2-1/2*x^2-x = 0

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

DELTA = 2

DELTA > 0

x = (2^(1/2)+1)/(-1/2*2) or x = (1-2^(1/2))/(-1/2*2)

x = -(2^(1/2)+1) or x = 2^(1/2)-1

(x+2^(1/2)+1)*(x-2^(1/2)+1) = 0

(x+2^(1/2)+1)*(x-2^(1/2)+1) = 0

( x+2^(1/2)+1 )

x+2^(1/2)+1 = 0 // - 2^(1/2)+1

x = -(2^(1/2)+1)

( x-2^(1/2)+1 )

x-2^(1/2)+1 = 0 // - 1-2^(1/2)

x = -(1-2^(1/2))

x = 2^(1/2)-1

x in { -(2^(1/2)+1), 2^(1/2)-1 }

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