What is the answer to 2x^3-3x=sqrt(1-x^2)(1-6x) ?

The answer to 2x^3-3x=sqrt(1-x^2)(1-6x) is x\approx 0.32765…,x\approx-0.98884…,x\approx 0.97536…

Solve for x: 2x^3-3x=sqrt(1-x^2)(1-6x)

The solution is x\approx 0.32765…,x\approx-0.98884…,x\approx 0.97536…

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2 x^{3} - 3 x = 1 - x^{2} (1 - 6 x)

x \approx 0.32765 \dots, x \approx - 0.98884 \dots, x \approx 0.97536 \dots

Solution steps

2 x^{3} - 3 x = 1 - x^{2} (1 - 6 x)

Expand

1 - x^{2} (1 - 6 x) : 1 - x^{2} - 6 1 - x^{2} x

2 x^{3} - 3 x = 1 - x^{2} - 6 1 - x^{2} x

Factor

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

Factor

1 - x^{2} - 6 1 - x^{2} x : - (6 x - 1) - (x + 1) (x - 1)

x (2 x + 3) (2 x - 3) = - (6 x - 1) - (x + 1) (x - 1)

Square both sides:

4 x^{6} - 12 x^{4} + 9 x^{2} = - 36 x^{4} + 12 x^{3} + 35 x^{2} - 12 x + 1

4 x^{6} - 12 x^{4} + 9 x^{2} = - 36 x^{4} + 12 x^{3} + 35 x^{2} - 12 x + 1

Solve

4 x^{6} - 12 x^{4} + 9 x^{2} = - 36 x^{4} + 12 x^{3} + 35 x^{2} - 12 x + 1 : x \approx 0.11118 \dots, x \approx 0.32765 \dots, x \approx - 0.98884 \dots, x \approx 0.97536 \dots

x \approx 0.11118 \dots, x \approx 0.32765 \dots, x \approx - 0.98884 \dots, x \approx 0.97536 \dots

Verify Solutions:

x \approx 0.11118 \dots

False

, x \approx 0.32765 \dots

True

, x \approx - 0.98884 \dots

True

, x \approx 0.97536 \dots

True

The solutions are

x \approx 0.32765 \dots, x \approx - 0.98884 \dots, x \approx 0.97536 \dots

2 a = 8

x - 2 = x + 2

- 8 - 2 a = 0

x - 16 - 6 x = 0

20 = \frac{5 ^{2} p}{5}

What is the answer to 2x^3-3x=sqrt(1-x^2)(1-6x) ?
The answer to 2x^3-3x=sqrt(1-x^2)(1-6x) is x\approx 0.32765…,x\approx-0.98884…,x\approx 0.97536…
Solve for x: 2x^3-3x=sqrt(1-x^2)(1-6x)
The solution is x\approx 0.32765…,x\approx-0.98884…,x\approx 0.97536…