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

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


x in (-oo:+oo)

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

abs(x^2-(1/4))-2 = 0

abs(x^2-1/4)-2 = 0

abs(x^2-1/4)-2 = 0

x in (-oo:+oo)

abs(x^2-1/4)

x^2-1/4 >= 0

1*x^2 >= 1/4

1*x^2 >= 1/4 // : 1

x^2 >= 1/4/1

x^2 >= 1/4

x^2 >= 1/4 // ^ 1/2

abs(x) >= 1/2

x in (-oo:-1/2> U <1/2:+oo)

x in (-oo:-1/2> U <1/2:+oo)

x^2-1/4-2 = 0

x in (-1/2:1/2)

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

abs(x^2-1/4)-2 = 0

/| -x^2-(-1/4)-2 = 0 i x in (-1/2:1/2)| x^2-1/4-2 = 0 i x in (-oo:-1/2> U <1/2:+oo)

x in (-1/2:1/2)

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

-1*x^2 = 7/4 // : -1

x^2 = -7/4

x in (-oo:-1/2> U <1/2:+oo)

x^2-1/4-2 = 0

1*x^2 = 9/4 // : 1

x^2 = 9/4

x^2 = 9/4 // ^ 1/2

abs(x) = 3/2

x = 3/2 or x = -3/2

x in { 3/2, -3/2 }

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