(x-1/2)^2=41/4

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Solution for (x-1/2)^2=41/4 equation:


x in (-oo:+oo)

(x-(1/2))^2 = 41/4 // - 41/4

(x-(1/2))^2-(41/4) = 0

(x-1/2)^2-41/4 = 0

(4*(x-1/2)^2)/4-41/4 = 0

4*(x-1/2)^2-41 = 0

4*x^2-4*x-40 = 0

4*x^2-4*x-40 = 0

4*(x^2-x-10) = 0

x^2-x-10 = 0

DELTA = (-1)^2-(-10*1*4)

DELTA = 41

DELTA > 0

x = (41^(1/2)+1)/(1*2) or x = (1-41^(1/2))/(1*2)

x = (41^(1/2)+1)/2 or x = (1-41^(1/2))/2

4*(x-((1-41^(1/2))/2))*(x-((41^(1/2)+1)/2)) = 0

(4*(x-((1-41^(1/2))/2))*(x-((41^(1/2)+1)/2)))/4 = 0

(4*(x-((1-41^(1/2))/2))*(x-((41^(1/2)+1)/2)))/4 = 0 // * 4

4*(x-((1-41^(1/2))/2))*(x-((41^(1/2)+1)/2)) = 0

( x-((1-41^(1/2))/2) )

x-((1-41^(1/2))/2) = 0 // + (1-41^(1/2))/2

x = (1-41^(1/2))/2

( x-((41^(1/2)+1)/2) )

x-((41^(1/2)+1)/2) = 0 // + (41^(1/2)+1)/2

x = (41^(1/2)+1)/2

x in { (1-41^(1/2))/2, (41^(1/2)+1)/2 }

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