1/4(x-3)^2-2

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Solution for 1/4(x-3)^2-2 equation: 


x in (-oo:+oo)

(1/4)*(x-3)^2-2 = 0

1/4*(x-3)^2-2 = 0

1/4*(x-3)^2-2 = 0

1/4*x^2-3/2*x+1/4 = 0

1/4*x^2-3/2*x+1/4 = 0

1/2*(1/2*x^2-3*x+1/2) = 0

1/2*x^2-3*x+1/2 = 0

DELTA = (-3)^2-(1/2*1/2*4)

DELTA = 8

DELTA > 0

x = (8^(1/2)+3)/(1/2*2) or x = (3-8^(1/2))/(1/2*2)

x = 2*2^(1/2)+3 or x = 3-2*2^(1/2)

1/2*(x+2*2^(1/2)-3)*(x-2*2^(1/2)-3) = 0

1/2*(x+2*2^(1/2)-3)*(x-2*2^(1/2)-3) = 0

( 1/2 )

1/2 = 0

x belongs to the empty set

( x+2*2^(1/2)-3 )

x+2*2^(1/2)-3 = 0 // - 2*2^(1/2)-3

x = -(2*2^(1/2)-3)

x = 3-(2*2^(1/2))

( x-2*2^(1/2)-3 )

x-2*2^(1/2)-3 = 0 // + -2*2^(1/2)-3

x = -(-2*2^(1/2)-3)

x = 3-(-2*2^(1/2))

x in { 3-(2*2^(1/2)), 3-(-2*2^(1/2)) }

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