What is the answer to 3x-x^2+(x+2)sqrt(9-x^2)=0 ?

The answer to 3x-x^2+(x+2)sqrt(9-x^2)=0 is x=3,x\approx-0.85456…

Solve for x: 3x-x^2+(x+2)sqrt(9-x^2)=0

The solution is x=3,x\approx-0.85456…

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3 x - x^{2} + (x + 2) 9 - x^{2} = 0

x = 3, x \approx - 0.85456 \dots

Solution steps

3 x - x^{2} + (x + 2) 9 - x^{2} = 0

Expand

3 x - x^{2} + (x + 2) 9 - x^{2} : 3 x - x^{2} + 9 - x^{2} x + 2 9 - x^{2}

3 x - x^{2} + 9 - x^{2} x + 2 9 - x^{2} = 0

Move

3 x

to the right side

- x^{2} + 9 - x^{2} x + 2 9 - x^{2} = - 3 x

Move

x^{2}

to the right side

9 - x^{2} x + 2 9 - x^{2} = - 3 x + x^{2}

Factor

9 - x^{2} x + 2 9 - x^{2} : 9 - x^{2} (x + 2)

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

Square both sides:

- x^{4} - 4 x^{3} + 5 x^{2} + 36 x + 36 = 9 x^{2} - 6 x^{3} + x^{4}

- x^{4} - 4 x^{3} + 5 x^{2} + 36 x + 36 = 9 x^{2} - 6 x^{3} + x^{4}

Solve

- x^{4} - 4 x^{3} + 5 x^{2} + 36 x + 36 = 9 x^{2} - 6 x^{3} + x^{4} : x = 3, x \approx - 0.85456 \dots

x = 3, x \approx - 0.85456 \dots

Verify Solutions:

x = 3

True

, x \approx - 0.85456 \dots

True

The solutions are

x = 3, x \approx - 0.85456 \dots

x - 2 x - 6 = 7

x + 1 = x^{3} - 1

12 + 1 - 4 x = 15

x, x + y + 2 x y = 36

5.12 = 3.3 x^{1.7}

What is the answer to 3x-x^2+(x+2)sqrt(9-x^2)=0 ?
The answer to 3x-x^2+(x+2)sqrt(9-x^2)=0 is x=3,x\approx-0.85456…
Solve for x: 3x-x^2+(x+2)sqrt(9-x^2)=0
The solution is x=3,x\approx-0.85456…