(5-x)^(1/2)-2x

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Solution for (5-x)^(1/2)-2x equation: 


D( x )

5-x < 0

5-x < 0

5-x < 0

5-x < 0

-x < -5 // * -1

x > 5

x in (-oo:5>

(5-x)^(1/2)-(2*x) = 0

(5-x)^(1/2)-2*x = 0

(5-x)^(1/2) = -2*x // + -2*x

(5-x)^(1/2) = -(-2*x) // ^ 2

abs(5-x) = (-(-2*x))^2 // - (-(-2*x))^2

abs(5-x)-(-(-2*x))^2 = 0

x in (-oo:+oo)

abs(5-x)

5-x >= 0

5-x >= 0

-x >= -5 // * -1

x <= 5

x in (-oo:5>

5-(-(-2*x))^2-x = 0

x in (5:+oo)

x-(-(-2*x))^2-5 = 0

abs(5-x)-(-(-2*x))^2 = 0


/
| 5-(-(-2*x))^2-x = 0 i x in (-oo:5>
| x-(-(-2*x))^2-5 = 0 i x in (5:+oo)


x in (-oo:5>

5-(-(-2*x))^2-x = 0

5-4*x^2-x = 0

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

DELTA = 81

DELTA > 0

x = (81^(1/2)+1)/(-4*2) or x = (1-81^(1/2))/(-4*2)

x = -5/4 or x = 1

x in (5:+oo)

x-(-(-2*x))^2-5 = 0

x-4*x^2-5 = 0

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

DELTA = -79

DELTA < 0

x in { -5/4, 1 }

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