What are the solutions to the equation x^3-5x+6=2.2 ?

The solutions to the equation x^3-5x+6=2.2 are x\approx 0.91142…,x\approx 1.63641…,x\approx-2.54783…

Find the zeros of x^3-5x+6=2.2

The zeros of x^3-5x+6=2.2 are x\approx 0.91142…,x\approx 1.63641…,x\approx-2.54783…

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x^{3} - 5 x + 6 = 2.2

x \approx 0.91142 \dots, x \approx 1.63641 \dots, x \approx - 2.54783 \dots

Solution steps

x^{3} - 5 x + 6 = 2.2

Multiply both sides by

10

10 x^{3} - 50 x + 60 = 22

Move

22

to the left side

10 x^{3} - 50 x + 38 = 0

Find one solution for

10 x^{3} - 50 x + 38 = 0

using Newton-Raphson:

x \approx 0.91142 \dots

Apply long division:

\frac{10 x ^{3} - 50 x + 38}{x - 0.91142 \dots} = 10 x^{2} + 9.11421 \dots x - 41.69310 \dots

10 x^{2} + 9.11421 \dots x - 41.69310 \dots \approx 0

Find one solution for

10 x^{2} + 9.11421 \dots x - 41.69310 \dots = 0

using Newton-Raphson:

x \approx 1.63641 \dots

Apply long division:

\frac{10 x ^{2} + 9.11421 \dots x - 41.69310 \dots}{x - 1.63641 \dots} = 10 x + 25.47834 \dots

10 x + 25.47834 \dots \approx 0

x \approx - 2.54783 \dots

The solutions are

x \approx 0.91142 \dots, x \approx 1.63641 \dots, x \approx - 2.54783 \dots

x + x^{2} + 400 x^{3} = 11500

6 x^{4} - x^{3} - 22 x^{2} + 11 x + 6 = 0

4 x^{4} - 349 x^{2} + 2025 = 0

y, x^{3} + y^{3} = x

- 2 x^{3} - 9 x^{2} - 12 x - 4 = 0

What are the solutions to the equation x^3-5x+6=2.2 ?
The solutions to the equation x^3-5x+6=2.2 are x\approx 0.91142…,x\approx 1.63641…,x\approx-2.54783…
Find the zeros of x^3-5x+6=2.2
The zeros of x^3-5x+6=2.2 are x\approx 0.91142…,x\approx 1.63641…,x\approx-2.54783…