What are the solutions to the equation -6x^6=2x-9 ?

The solutions to the equation -6x^6=2x-9 are x\approx 1.02480…,x\approx-1.10995…

Find the zeros of -6x^6=2x-9

The zeros of -6x^6=2x-9 are x\approx 1.02480…,x\approx-1.10995…

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- 6 x^{6} = 2 x - 9

x \approx 1.02480 \dots, x \approx - 1.10995 \dots

Solution steps

- 6 x^{6} = 2 x - 9

Move

9

to the left side

- 6 x^{6} + 9 = 2 x

Move

2 x

to the left side

- 6 x^{6} + 9 - 2 x = 0

Write in the standard form

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

- 6 x^{6} - 2 x + 9 = 0

Find one solution for

- 6 x^{6} - 2 x + 9 = 0

using Newton-Raphson:

x \approx 1.02480 \dots

Apply long division:

\frac{- 6 x ^{6} - 2 x + 9}{x - 1.02480 \dots} = - 6 x^{5} - 6.14885 \dots x^{4} - 6.30140 \dots x^{3} - 6.45773 \dots x^{2} - 6.61794 \dots x - 8.78212 \dots

- 6 x^{5} - 6.14885 \dots x^{4} - 6.30140 \dots x^{3} - 6.45773 \dots x^{2} - 6.61794 \dots x - 8.78212 \dots \approx 0

Find one solution for

- 6 x^{5} - 6.14885 \dots x^{4} - 6.30140 \dots x^{3} - 6.45773 \dots x^{2} - 6.61794 \dots x - 8.78212 \dots = 0

using Newton-Raphson:

x \approx - 1.10995 \dots

Apply long division:

\frac{- 6 x ^{5} - 6.14885 \dots x ^{4} - 6.30140 \dots x ^{3} - 6.45773 \dots x ^{2} - 6.61794 \dots x - 8.78212 \dots}{x + 1.10995 \dots} = - 6 x^{4} + 0.51089 \dots x^{3} - 6.86846 \dots x^{2} + 1.16597 \dots x - 7.91212 \dots

- 6 x^{4} + 0.51089 \dots x^{3} - 6.86846 \dots x^{2} + 1.16597 \dots x - 7.91212 \dots \approx 0

Find one solution for

- 6 x^{4} + 0.51089 \dots x^{3} - 6.86846 \dots x^{2} + 1.16597 \dots x - 7.91212 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.02480 \dots, x \approx - 1.10995 \dots

\frac{7}{x + 3} > - 5

4 x - 3 (2 x + 1) \leq 4 (x - 3)

x^{2} - 6 x + 14 = 0

6 - 5

3 (- 2) + 4

What are the solutions to the equation -6x^6=2x-9 ?
The solutions to the equation -6x^6=2x-9 are x\approx 1.02480…,x\approx-1.10995…
Find the zeros of -6x^6=2x-9
The zeros of -6x^6=2x-9 are x\approx 1.02480…,x\approx-1.10995…