1/2(x-4)^2=7

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Solution for 1/2(x-4)^2=7 equation: 


x in (-oo:+oo)

(1/2)*(x-4)^2 = 7 // - 7

(1/2)*(x-4)^2-7 = 0

1/2*(x-4)^2-7 = 0

1/2*(x-4)^2-7 = 0

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

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

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

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

DELTA = 14

DELTA > 0

x = (14^(1/2)+4)/(1/2*2) or x = (4-14^(1/2))/(1/2*2)

x = 14^(1/2)+4 or x = 4-14^(1/2)

(x+14^(1/2)-4)*(x-14^(1/2)-4) = 0

(x+14^(1/2)-4)*(x-14^(1/2)-4) = 0

( x+14^(1/2)-4 )

x+14^(1/2)-4 = 0 // - 14^(1/2)-4

x = -(14^(1/2)-4)

x = 4-14^(1/2)

( x-14^(1/2)-4 )

x-14^(1/2)-4 = 0 // + 14^(1/2)+4

x = 14^(1/2)+4

x in { 4-14^(1/2), 14^(1/2)+4 }

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