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

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

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

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

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\frac{1}{2} x = x 1 - x^{2}

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

Decimal Notation

x = 0, x = 0.86602 \dots, x = - 0.86602 \dots

Solution steps

\frac{1}{2} x = x 1 - x^{2}

Multiply both sides by

2

\frac{1}{2} x \cdot 2 = x 1 - x^{2} \cdot 2

Simplify

x = x 1 - x^{2} \cdot 2

Move

x 1 - x^{2} 2

to the left side

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

Factor

x - x 1 - x^{2} \cdot 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}

2 x - 1 - x + 2 = 0

2 u + 15 = 4 u + 3

x^{2} - 5 - 4 - x = 0

9 - 11 x = 8

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