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

The answer to x=2xsqrt(1-x^2) is x=0,x=(sqrt(3))/2 ,x=-(sqrt(3))/2

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

The solution is x=0,x=(sqrt(3))/2 ,x=-(sqrt(3))/2

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x = 2 x 1 - x^{2}

x = 0, x = \frac{3}{2}, x = - \frac{3}{2}

Solution steps

x = 2 x 1 - x^{2}

Move

2 x 1 - x^{2}

to the left side

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

Factor

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

- x (2 1 - x^{2} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

2 1 - x^{2} - 1 = 0 : x = \frac{3}{2}, x = - \frac{3}{2}

x = 0, x = \frac{3}{2}, x = - \frac{3}{2}

Verify Solutions:

x = 0

True

, x = \frac{3}{2}

True

, x = - \frac{3}{2}

True

The solutions are

x = 0, x = \frac{3}{2}, x = - \frac{3}{2}

- 3 2 x + (- 4) 2 = 6

2 x^{\frac{2}{5}} - 43 = - 25

3 x - 17 x^{\frac{1}{2}} + 10 = 0

5 - x = 4

What is the answer to x=2xsqrt(1-x^2) ?
The answer to x=2xsqrt(1-x^2) is x=0,x=(sqrt(3))/2 ,x=-(sqrt(3))/2
Solve for x: x=2xsqrt(1-x^2)
The solution is x=0,x=(sqrt(3))/2 ,x=-(sqrt(3))/2