8(4x)^(1/2)=7x-14

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Solution for 8(4x)^(1/2)=7x-14 equation:


D( x )

4*x < 0

4*x < 0

4*x < 0

4*x+0 < 0 // - 0

4*x < 0 // : 4

x < 0/4

x < 0

x in <0:+oo)

8*(4*x)^(1/2) = 7*x-14 // - 7*x-14

8*(4*x)^(1/2)-(7*x)+14 = 0

8*(4*x)^(1/2)-7*x+14 = 0

16*x^(1/2)-7*x+14 = 0

t_1 = x^(1/2)

16*t_1^1-7*t_1^2+14 = 0

16*t_1-7*t_1^2+14 = 0

DELTA = 16^2-(-7*4*14)

DELTA = 648

DELTA > 0

t_1 = (648^(1/2)-16)/(-7*2) or t_1 = (-648^(1/2)-16)/(-7*2)

t_1 = (18*2^(1/2)-16)/(-14) or t_1 = (-18*2^(1/2)-16)/(-14)

t_1 = (18*2^(1/2)-16)/(-14)

x^(1/2)-((18*2^(1/2)-16)/(-14)) = 0

1*x^(1/2) = (18*2^(1/2)-16)/(-14) // : 1

x^(1/2) = (18*2^(1/2)-16)/(-14)

( (18*2^(1/2)-16)/(-14) < 0 i 1/2 in (0:1) ) => x należy do O

t_1 = (-18*2^(1/2)-16)/(-14)

x^(1/2)-((-18*2^(1/2)-16)/(-14)) = 0

1*x^(1/2) = (-18*2^(1/2)-16)/(-14) // : 1

x^(1/2) = (-18*2^(1/2)-16)/(-14)

x^(1/2) = (-18*2^(1/2)-16)/(-14) // ^ 2

x = ((-18*2^(1/2)-16)^2)/196

x = ((-18*2^(1/2)-16)^2)/196

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