What are the solutions to the equation -6x^4+5x^3+6x^2=11x+5 ?

The solutions to the equation -6x^4+5x^3+6x^2=11x+5 are x\approx-0.40962…,x\approx-1.05400…

Find the zeros of -6x^4+5x^3+6x^2=11x+5

The zeros of -6x^4+5x^3+6x^2=11x+5 are x\approx-0.40962…,x\approx-1.05400…

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- 6 x^{4} + 5 x^{3} + 6 x^{2} = 11 x + 5

x \approx - 0.40962 \dots, x \approx - 1.05400 \dots

Solution steps

- 6 x^{4} + 5 x^{3} + 6 x^{2} = 11 x + 5

Move

5

to the left side

- 6 x^{4} + 5 x^{3} + 6 x^{2} - 5 = 11 x

Move

11 x

to the left side

- 6 x^{4} + 5 x^{3} + 6 x^{2} - 5 - 11 x = 0

Write in the standard form

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

- 6 x^{4} + 5 x^{3} + 6 x^{2} - 11 x - 5 = 0

Find one solution for

- 6 x^{4} + 5 x^{3} + 6 x^{2} - 11 x - 5 = 0

using Newton-Raphson:

x \approx - 0.40962 \dots

Apply long division:

\frac{- 6 x ^{4} + 5 x ^{3} + 6 x ^{2} - 11 x - 5}{x + 0.40962 \dots} = - 6 x^{3} + 7.45772 \dots x^{2} + 2.94515 \dots x - 12.20639 \dots

- 6 x^{3} + 7.45772 \dots x^{2} + 2.94515 \dots x - 12.20639 \dots \approx 0

Find one solution for

- 6 x^{3} + 7.45772 \dots x^{2} + 2.94515 \dots x - 12.20639 \dots = 0

using Newton-Raphson:

x \approx - 1.05400 \dots

Apply long division:

\frac{- 6 x ^{3} + 7.45772 \dots x ^{2} + 2.94515 \dots x - 12.20639 \dots}{x + 1.05400 \dots} = - 6 x^{2} + 13.78177 \dots x - 11.58093 \dots

- 6 x^{2} + 13.78177 \dots x - 11.58093 \dots \approx 0

Find one solution for

- 6 x^{2} + 13.78177 \dots x - 11.58093 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.40962 \dots, x \approx - 1.05400 \dots

(z^{2} + 7)^{2} + (z^{2} + 7) - 72 = 0

y, x = (y - 1)^{3}

4 x^{3} - 7 x^{2} - 2 x = 0

2 x^{3} + 2 x^{2} + 2 x + 1 = 0

x^{3} - 3 x = 3

What are the solutions to the equation -6x^4+5x^3+6x^2=11x+5 ?
The solutions to the equation -6x^4+5x^3+6x^2=11x+5 are x\approx-0.40962…,x\approx-1.05400…
Find the zeros of -6x^4+5x^3+6x^2=11x+5
The zeros of -6x^4+5x^3+6x^2=11x+5 are x\approx-0.40962…,x\approx-1.05400…