(x-1/4)^2=41/16

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Solution for (x-1/4)^2=41/16 equation:


x in (-oo:+oo)

(x-(1/4))^2 = 41/16 // - 41/16

(x-(1/4))^2-(41/16) = 0

(x-1/4)^2-41/16 = 0

(16*(x-1/4)^2)/16-41/16 = 0

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

16*x^2-8*x-40 = 0

16*x^2-8*x-40 = 0

8*(2*x^2-x-5) = 0

2*x^2-x-5 = 0

DELTA = (-1)^2-(-5*2*4)

DELTA = 41

DELTA > 0

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

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

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

(8*(x-((1-41^(1/2))/4))*(x-((41^(1/2)+1)/4)))/16 = 0

(8*(x-((1-41^(1/2))/4))*(x-((41^(1/2)+1)/4)))/16 = 0 // * 16

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

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

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

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

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

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

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

x in { (1-41^(1/2))/4, (41^(1/2)+1)/4 }

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