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D( x )
2*x-7 < 0
2*x-7 < 0
2*x-7 < 0
2*x-7 < 0 // + 7
2*x < 7 // : 2
x < 7/2
x in <7/2:+oo)
x-5 = (2*x-7)^(1/2) // - (2*x-7)^(1/2)
x-(2*x-7)^(1/2)-5 = 0
-(2*x-7)^(1/2) = x-5 // - x-5
-(2*x-7)^(1/2) = -(x-5) // ^ 2
abs(2*x-7) = (-(x-5))^2 // - (-(x-5))^2
abs(2*x-7)-(-(x-5))^2 = 0
x in (-oo:+oo)
abs(2*x-7)
2*x-7 >= 0
2*x-7 >= 0 // + 7
2*x >= 7 // : 2
x >= 7/2
x in <7/2:+oo)
2*x-(-(x-5))^2-7 = 0
x in (-oo:7/2)
7-(-(x-5))^2-(2*x) = 0
abs(2*x-7)-(-(x-5))^2 = 0
/ | 7-(-(x-5))^2-(2*x) = 0 i x in (-oo:7/2) | 2*x-(-(x-5))^2-7 = 0 i x in <7/2:+oo)
x in (-oo:7/2)
7-(-(x-5))^2-(2*x) = 0
7-1*(5-x)^2-2*x = 0
7-1*(5-x)^2-2*x = 0
8*x-x^2-25+7 = 0
8*x-x^2-18 = 0
8*x-x^2-18 = 0
8*x-x^2-18 = 0
DELTA = 8^2-(-18*(-1)*4)
DELTA = -8
DELTA < 0
1 = 0
1 = 0
x in <7/2:+oo)
2*x-(-(x-5))^2-7 = 0
2*x-1*(5-x)^2-7 = 0
2*x-1*(5-x)^2-7 = 0
12*x-x^2-25-7 = 0
12*x-x^2-32 = 0
12*x-x^2-32 = 0
12*x-x^2-32 = 0
DELTA = 12^2-(-32*(-1)*4)
DELTA = 16
DELTA > 0
x = (16^(1/2)-12)/(-1*2) or x = (-16^(1/2)-12)/(-1*2)
x = 4 or x = 8
(x-4)*(x-8) = 0
(x-4)*(x-8) = 0
( x-4 )
x-4 = 0 // + 4
x = 4
( x-8 )
x-8 = 0 // + 8
x = 8
x in { 4, 8 }
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