w-4=(32-2w)^(1/2)

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Solution for w-4=(32-2w)^(1/2) equation:


D( w )

32-(2*w) < 0

32-(2*w) < 0

32-(2*w) < 0

32-2*w < 0

32-2*w < 0 // - 32

-2*w < -32 // : -2

w > -32/(-2)

w > 16

w in (-oo:16>

w-4 = (32-(2*w))^(1/2) // - (32-(2*w))^(1/2)

w-(32-(2*w))^(1/2)-4 = 0

w-(32-2*w)^(1/2)-4 = 0

-(32-2*w)^(1/2) = w-4 // - w-4

-(32-2*w)^(1/2) = -(w-4) // ^ 2

abs(32-2*w) = (-(w-4))^2 // - (-(w-4))^2

abs(32-2*w)-(-(w-4))^2 = 0

w in (-oo:+oo)

abs(32-2*w)

32-2*w >= 0

32-2*w >= 0 // - 32

-2*w >= -32 // : -2

w <= -32/(-2)

w <= 16

w in (-oo:16>

32-(-(w-4))^2-2*w = 0

w in (16:+oo)

-(-(w-4))^2-(-2*w)-32 = 0

abs(32-2*w)-(-(w-4))^2 = 0

/ | 32-(-(w-4))^2-2*w = 0 i w in (-oo:16> | -(-(w-4))^2-(-2*w)-32 = 0 i w in (16:+oo)

w in (-oo:16>

32-(-(w-4))^2-2*w = 0

32-1*(4-w)^2-2*w = 0

32-1*(4-w)^2-2*w = 0

6*w-w^2-16+32 = 0

6*w-w^2+16 = 0

6*w-w^2+16 = 0

6*w-w^2+16 = 0

DELTA = 6^2-(-1*4*16)

DELTA = 100

DELTA > 0

w = (100^(1/2)-6)/(-1*2) or w = (-100^(1/2)-6)/(-1*2)

w = -2 or w = 8

(w+2)*(w-8) = 0

(w+2)*(w-8) = 0

( w+2 )

w+2 = 0 // - 2

w = -2

( w-8 )

w-8 = 0 // + 8

w = 8

w in (16:+oo)

-(-(w-4))^2-(-2*w)-32 = 0

2*w-1*(4-w)^2-32 = 0

2*w-1*(4-w)^2-32 = 0

10*w-w^2-32-16 = 0

10*w-w^2-48 = 0

10*w-w^2-48 = 0

10*w-w^2-48 = 0

DELTA = 10^2-(-48*(-1)*4)

DELTA = -92

DELTA < 0

1 = 0

1 = 0

w in { -2, 8 }

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