What is the answer to x(1-x)=2x-xsqrt(1-x)-x ?

The answer to x(1-x)=2x-xsqrt(1-x)-x is x=0,x=(-1+sqrt(5))/2

Solve for x: x(1-x)=2x-xsqrt(1-x)-x

The solution is x=0,x=(-1+sqrt(5))/2

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x (1 - x) = 2 x - x 1 - x - x

x = 0, x = \frac{- 1 + 5}{2}

Decimal Notation

x = 0, x = 0.61803 \dots

Solution steps

x (1 - x) = 2 x - x 1 - x - x

Subtract

2 x - x 1 - x - x

from both sides

x (1 - x) - (2 x - x 1 - x - x) = 2 x - x 1 - x - x - (2 x - x 1 - x - x)

Simplify

- x^{2} + 1 - x x = 0

Factor

- x^{2} + 1 - x x : x (- x + 1 - x)

x (- x + 1 - x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or - x + 1 - x = 0

Solve

- x + 1 - x = 0 : x = \frac{- 1 + 5}{2}

x = 0, x = \frac{- 1 + 5}{2}

Verify Solutions:

x = 0

True

, x = \frac{- 1 + 5}{2}

True

The solutions are

x = 0, x = \frac{- 1 + 5}{2}

19 - 3 x + x = 3

5 x - 6 - 16 = 0

36 x^{2} - 12 x + 1 = 5

3 = x^{2} + (- 1)^{2}

21 + q = 3 + q

What is the answer to x(1-x)=2x-xsqrt(1-x)-x ?
The answer to x(1-x)=2x-xsqrt(1-x)-x is x=0,x=(-1+sqrt(5))/2
Solve for x: x(1-x)=2x-xsqrt(1-x)-x
The solution is x=0,x=(-1+sqrt(5))/2