1/2(x-3)^2=16

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Solution for 1/2(x-3)^2=16 equation: 


x in (-oo:+oo)

(1/2)*(x-3)^2 = 16 // - 16

(1/2)*(x-3)^2-16 = 0

1/2*(x-3)^2-16 = 0

1/2*(x-3)^2-16 = 0

1/2*x^2-3*x-23/2 = 0

1/2*x^2-3*x-23/2 = 0

1/2*x^2-3*x-23/2 = 0

DELTA = (-3)^2-(-23/2*1/2*4)

DELTA = 32

DELTA > 0

x = (32^(1/2)+3)/(1/2*2) or x = (3-32^(1/2))/(1/2*2)

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

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

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

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

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

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

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

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

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

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

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

x in { 3-(4*2^(1/2)), 3-(-4*2^(1/2)) }

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