4x^2-64-256=25-(x-8)^2/4

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Solution for 4x^2-64-256=25-(x-8)^2/4 equation:


x in (-oo:+oo)

4*x^2-256-64 = 25-(((x-8)^2)/4) // - 25-(((x-8)^2)/4)

((x-8)^2)/4+4*x^2-256-64-25 = 0

((x-8)^2)/4+(4*4*x^2)/4+(-256*4)/4+(-64*4)/4+(-25*4)/4 = 0

(x-8)^2+4*4*x^2-256*4-64*4-25*4 = 0

17*x^2-16*x-1024-256-100+64 = 0

17*x^2-16*x-960-256-100 = 0

17*x^2-16*x-1216-100 = 0

17*x^2-16*x-1316 = 0

17*x^2-16*x-1316 = 0

17*x^2-16*x-1316 = 0

DELTA = (-16)^2-(-1316*4*17)

DELTA = 89744

DELTA > 0

x = (89744^(1/2)+16)/(2*17) or x = (16-89744^(1/2))/(2*17)

x = (4*5609^(1/2)+16)/34 or x = (16-4*5609^(1/2))/34

(x-((16-4*5609^(1/2))/34))*(x-((4*5609^(1/2)+16)/34)) = 0

((x-((16-4*5609^(1/2))/34))*(x-((4*5609^(1/2)+16)/34)))/4 = 0

((x-((16-4*5609^(1/2))/34))*(x-((4*5609^(1/2)+16)/34)))/4 = 0 // * 4

(x-((16-4*5609^(1/2))/34))*(x-((4*5609^(1/2)+16)/34)) = 0

( x-((16-4*5609^(1/2))/34) )

x-((16-4*5609^(1/2))/34) = 0 // + (16-4*5609^(1/2))/34

x = (16-4*5609^(1/2))/34

( x-((4*5609^(1/2)+16)/34) )

x-((4*5609^(1/2)+16)/34) = 0 // + (4*5609^(1/2)+16)/34

x = (4*5609^(1/2)+16)/34

x in { (16-4*5609^(1/2))/34, (4*5609^(1/2)+16)/34 }

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