What is the answer to x*sqrt(-2x^2+6x+1)=-4x^2+6x+1 ?

The answer to x*sqrt(-2x^2+6x+1)=-4x^2+6x+1 is x\approx-0.15470…,x\approx 1.14549…

Solve for x: x*sqrt(-2x^2+6x+1)=-4x^2+6x+1

The solution is x\approx-0.15470…,x\approx 1.14549…

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x \cdot - 2 x^{2} + 6 x + 1 = - 4 x^{2} + 6 x + 1

x \approx - 0.15470 \dots, x \approx 1.14549 \dots

Solution steps

x - 2 x^{2} + 6 x + 1 = - 4 x^{2} + 6 x + 1

Square both sides:

- 2 x^{4} + 6 x^{3} + x^{2} = 16 x^{4} - 48 x^{3} + 28 x^{2} + 12 x + 1

- 2 x^{4} + 6 x^{3} + x^{2} = 16 x^{4} - 48 x^{3} + 28 x^{2} + 12 x + 1

Solve

- 2 x^{4} + 6 x^{3} + x^{2} = 16 x^{4} - 48 x^{3} + 28 x^{2} + 12 x + 1 : x \approx - 0.14549 \dots, x \approx - 0.15470 \dots, x \approx 1.14549 \dots, x \approx 2.15470 \dots

x \approx - 0.14549 \dots, x \approx - 0.15470 \dots, x \approx 1.14549 \dots, x \approx 2.15470 \dots

Verify Solutions:

x \approx - 0.14549 \dots

False

, x \approx - 0.15470 \dots

True

, x \approx 1.14549 \dots

True

, x \approx 2.15470 \dots

False

The solutions are

x \approx - 0.15470 \dots, x \approx 1.14549 \dots

a^{\frac{1}{2}} = 5

x = 9

x^{2} + 4 x^{2} - 21 = 0

3 x + 1 - 2 x - 1 = 1

8 x - 12 + 18 x - 27 - 32 x - 48 = 7

What is the answer to x*sqrt(-2x^2+6x+1)=-4x^2+6x+1 ?
The answer to x*sqrt(-2x^2+6x+1)=-4x^2+6x+1 is x\approx-0.15470…,x\approx 1.14549…
Solve for x: x*sqrt(-2x^2+6x+1)=-4x^2+6x+1
The solution is x\approx-0.15470…,x\approx 1.14549…