What is the answer to x=2xsqrt(16-x^2) ?

The answer to x=2xsqrt(16-x^2) is x=0,x=(3sqrt(7))/2 ,x=-(3sqrt(7))/2

Solve for x: x=2xsqrt(16-x^2)

The solution is x=0,x=(3sqrt(7))/2 ,x=-(3sqrt(7))/2

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x = 2 x 16 - x^{2}

x = 0, x = \frac{3 7}{2}, x = - \frac{3 7}{2}

Decimal Notation

x = 0, x = 3.96862 \dots, x = - 3.96862 \dots

Solution steps

x = 2 x 16 - x^{2}

Move

2 x 16 - x^{2}

to the left side

x - 2 x 16 - x^{2} = 0

Factor

x - 2 x 16 - x^{2} : - x (2 16 - x^{2} - 1)

- x (2 16 - x^{2} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 2 16 - x^{2} - 1 = 0

Solve

2 16 - x^{2} - 1 = 0 : x = \frac{3 7}{2}, x = - \frac{3 7}{2}

x = 0, x = \frac{3 7}{2}, x = - \frac{3 7}{2}

Verify Solutions:

x = 0

True

, x = \frac{3 7}{2}

True

, x = - \frac{3 7}{2}

True

The solutions are

x = 0, x = \frac{3 7}{2}, x = - \frac{3 7}{2}

x + 6 = 3 x^{2} - 5 x - 5

4 x - 1 = 7

4 x - 1 = 9

9 x + 10 = x + 2

x - 5 x - 6 = 0

What is the answer to x=2xsqrt(16-x^2) ?
The answer to x=2xsqrt(16-x^2) is x=0,x=(3sqrt(7))/2 ,x=-(3sqrt(7))/2
Solve for x: x=2xsqrt(16-x^2)
The solution is x=0,x=(3sqrt(7))/2 ,x=-(3sqrt(7))/2