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Popular >

2x^3-4x-7x=-x^2+x+3

Solution

2 x^{3} - 4 x - 7 x = - x^{2} + x + 3

Solution

x \approx - 0.24742 \dots, x \approx 2.33916 \dots, x \approx - 2.59173 \dots

Solution steps

2 x^{3} - 4 x - 7 x = - x^{2} + x + 3

Refine

2 x^{3} - 11 x = - x^{2} + x + 3

Move

3

to the left side

2 x^{3} - 11 x - 3 = - x^{2} + x

Move

x

to the left side

2 x^{3} - 12 x - 3 = - x^{2}

Move

x^{2}

to the left side

2 x^{3} - 12 x - 3 + x^{2} = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

2 x^{3} + x^{2} - 12 x - 3 = 0

Find one solution for

2 x^{3} + x^{2} - 12 x - 3 = 0

using Newton-Raphson:

x \approx - 0.24742 \dots

Apply long division:

\frac{2 x ^{3} + x ^{2} - 12 x - 3}{x + 0.24742 \dots} = 2 x^{2} + 0.50515 \dots x - 12.12498 \dots

2 x^{2} + 0.50515 \dots x - 12.12498 \dots \approx 0

Find one solution for

2 x^{2} + 0.50515 \dots x - 12.12498 \dots = 0

using Newton-Raphson:

x \approx 2.33916 \dots

Apply long division:

\frac{2 x ^{2} + 0.50515 \dots x - 12.12498 \dots}{x - 2.33916 \dots} = 2 x + 5.18347 \dots

2 x + 5.18347 \dots \approx 0

x \approx - 2.59173 \dots

The solutions are

x \approx - 0.24742 \dots, x \approx 2.33916 \dots, x \approx - 2.59173 \dots

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48.46 x^{3} + 12.6 x - 0.005 = 0

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