(11((x-7)/2)^2)-20=101

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Solution for (11((x-7)/2)^2)-20=101 equation: 


x in (-oo:+oo)

11*((x-7)/2)^2-20 = 101 // - 101

11*((x-7)/2)^2-101-20 = 0

(11*(x-7)^2)/(2^2)-101-20 = 0

(11*(x-7)^2)/(2^2)+(-101*2^2)/(2^2)+(-20*2^2)/(2^2) = 0

11*(x-7)^2-101*2^2-20*2^2 = 0

11*x^2-154*x-80+135 = 0

11*x^2-154*x+55 = 0

11*x^2-154*x+55 = 0

11*(x^2-14*x+5) = 0

x^2-14*x+5 = 0

DELTA = (-14)^2-(1*4*5)

DELTA = 176

DELTA > 0

x = (176^(1/2)+14)/(1*2) or x = (14-176^(1/2))/(1*2)

x = (4*11^(1/2)+14)/2 or x = (14-4*11^(1/2))/2

11*(x-((14-4*11^(1/2))/2))*(x-((4*11^(1/2)+14)/2)) = 0

(11*(x-((14-4*11^(1/2))/2))*(x-((4*11^(1/2)+14)/2)))/(2^2) = 0

(11*(x-((14-4*11^(1/2))/2))*(x-((4*11^(1/2)+14)/2)))/(2^2) = 0 // * 4

11*(x-((14-4*11^(1/2))/2))*(x-((4*11^(1/2)+14)/2)) = 0

( 11 )

11 = 0

x belongs to the empty set

( x-((14-4*11^(1/2))/2) )

x-((14-4*11^(1/2))/2) = 0 // + (14-4*11^(1/2))/2

x = (14-4*11^(1/2))/2

( x-((4*11^(1/2)+14)/2) )

x-((4*11^(1/2)+14)/2) = 0 // + (4*11^(1/2)+14)/2

x = (4*11^(1/2)+14)/2

x in { (14-4*11^(1/2))/2, (4*11^(1/2)+14)/2 }

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