What are the solutions to the equation -5x^2+6x=8x^8-5x^4+1 ?

The solutions to the equation -5x^2+6x=8x^8-5x^4+1 are x\approx 0.19808…,x\approx 0.90934…

Find the zeros of -5x^2+6x=8x^8-5x^4+1

The zeros of -5x^2+6x=8x^8-5x^4+1 are x\approx 0.19808…,x\approx 0.90934…

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- 5 x^{2} + 6 x = 8 x^{8} - 5 x^{4} + 1

x \approx 0.19808 \dots, x \approx 0.90934 \dots

Solution steps

- 5 x^{2} + 6 x = 8 x^{8} - 5 x^{4} + 1

Switch sides

8 x^{8} - 5 x^{4} + 1 = - 5 x^{2} + 6 x

Move

6 x

to the left side

8 x^{8} - 5 x^{4} + 1 - 6 x = - 5 x^{2}

Move

5 x^{2}

to the left side

8 x^{8} - 5 x^{4} + 1 - 6 x + 5 x^{2} = 0

Write in the standard form

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

8 x^{8} - 5 x^{4} + 5 x^{2} - 6 x + 1 = 0

Find one solution for

8 x^{8} - 5 x^{4} + 5 x^{2} - 6 x + 1 = 0

using Newton-Raphson:

x \approx 0.19808 \dots

Apply long division:

\frac{8 x ^{8} - 5 x ^{4} + 5 x ^{2} - 6 x + 1}{x - 0.19808 \dots} = 8 x^{7} + 1.58467 \dots x^{6} + 0.31390 \dots x^{5} + 0.06217 \dots x^{4} - 4.98768 \dots x^{3} - 0.98798 \dots x^{2} + 4.80429 \dots x - 5.04834 \dots

8 x^{7} + 1.58467 \dots x^{6} + 0.31390 \dots x^{5} + 0.06217 \dots x^{4} - 4.98768 \dots x^{3} - 0.98798 \dots x^{2} + 4.80429 \dots x - 5.04834 \dots \approx 0

Find one solution for

8 x^{7} + 1.58467 \dots x^{6} + 0.31390 \dots x^{5} + 0.06217 \dots x^{4} - 4.98768 \dots x^{3} - 0.98798 \dots x^{2} + 4.80429 \dots x - 5.04834 \dots = 0

using Newton-Raphson:

x \approx 0.90934 \dots

Apply long division:

\frac{8 x ^{7} + 1.58467 \dots x ^{6} + 0.31390 \dots x ^{5} + 0.06217 \dots x ^{4} - 4.98768 \dots x ^{3} - 0.98798 \dots x ^{2} + 4.80429 \dots x - 5.04834 \dots}{x - 0.90934 \dots} = 8 x^{6} + 8.85943 \dots x^{5} + 8.37018 \dots x^{4} + 7.67357 \dots x^{3} + 1.99024 \dots x^{2} + 0.82183 \dots x + 5.55162 \dots

8 x^{6} + 8.85943 \dots x^{5} + 8.37018 \dots x^{4} + 7.67357 \dots x^{3} + 1.99024 \dots x^{2} + 0.82183 \dots x + 5.55162 \dots \approx 0

Find one solution for

8 x^{6} + 8.85943 \dots x^{5} + 8.37018 \dots x^{4} + 7.67357 \dots x^{3} + 1.99024 \dots x^{2} + 0.82183 \dots x + 5.55162 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.19808 \dots, x \approx 0.90934 \dots

x^{3} + 10 x^{2} + 29 x + 30 = 0

- 2 = 4 x^{3} + 5

x^{4} + 4 1^{2} + 400 = 0

2 x^{5} - 8 x^{4} - 10 x^{3} = 0

2 x^{3} + 6 x^{2} + x = 0

What are the solutions to the equation -5x^2+6x=8x^8-5x^4+1 ?
The solutions to the equation -5x^2+6x=8x^8-5x^4+1 are x\approx 0.19808…,x\approx 0.90934…
Find the zeros of -5x^2+6x=8x^8-5x^4+1
The zeros of -5x^2+6x=8x^8-5x^4+1 are x\approx 0.19808…,x\approx 0.90934…