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)^2-101-20 = 0

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

11*x^2-77*x-20+135/4 = 0

11*x^2-77*x+55/4 = 0

11*x^2-77*x+55/4 = 0

11*(x^2-7*x+5/4) = 0

x^2-7*x+5/4 = 0

DELTA = (-7)^2-(1*5/4*4)

DELTA = 44

DELTA > 0

x = (44^(1/2)+7)/(1*2) or x = (7-44^(1/2))/(1*2)

x = (2*11^(1/2)+7)/2 or x = (7-2*11^(1/2))/2

11*(x-((7-2*11^(1/2))/2))*(x-((2*11^(1/2)+7)/2)) = 0

11*(x-((7-2*11^(1/2))/2))*(x-((2*11^(1/2)+7)/2)) = 0

( 11 )

11 = 0

x belongs to the empty set

( x-((2*11^(1/2)+7)/2) )

x-((2*11^(1/2)+7)/2) = 0 // + (2*11^(1/2)+7)/2

x = (2*11^(1/2)+7)/2

( x-((7-2*11^(1/2))/2) )

x-((7-2*11^(1/2))/2) = 0 // + (7-2*11^(1/2))/2

x = (7-2*11^(1/2))/2

x in { (2*11^(1/2)+7)/2, (7-2*11^(1/2))/2 }

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