1/2(x+3)2=5

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Solution for 1/2(x+3)2=5 equation: 


x in (-oo:+oo)

(1/2)*(x+3)^2 = 5 // - 5

(1/2)*(x+3)^2-5 = 0

1/2*(x+3)^2-5 = 0

1/2*(x+3)^2-5 = 0

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

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 = 10

DELTA > 0

x = (10^(1/2)-3)/(1/2*2) or x = (-10^(1/2)-3)/(1/2*2)

x = 10^(1/2)-3 or x = -(10^(1/2)+3)

(x+10^(1/2)+3)*(x-10^(1/2)+3) = 0

(x+10^(1/2)+3)*(x-10^(1/2)+3) = 0

( x+10^(1/2)+3 )

x+10^(1/2)+3 = 0 // - 10^(1/2)+3

x = -(10^(1/2)+3)

( x-10^(1/2)+3 )

x-10^(1/2)+3 = 0 // - 3-10^(1/2)

x = -(3-10^(1/2))

x = 10^(1/2)-3

x in { -(10^(1/2)+3), 10^(1/2)-3 }

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