What are the solutions to the equation 2x=(35x^6)-178 ?

The solutions to the equation 2x=(35x^6)-178 are x\approx-1.30813…,x\approx 1.31457…

Find the zeros of 2x=(35x^6)-178

The zeros of 2x=(35x^6)-178 are x\approx-1.30813…,x\approx 1.31457…

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2 x = (35 x^{6}) - 178

x \approx - 1.30813 \dots, x \approx 1.31457 \dots

Solution steps

2 x = (35 x^{6}) - 178

Refine

2 x = 35 x^{6} - 178

Switch sides

35 x^{6} - 178 = 2 x

Move

2 x

to the left side

35 x^{6} - 178 - 2 x = 0

Write in the standard form

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

35 x^{6} - 2 x - 178 = 0

Find one solution for

35 x^{6} - 2 x - 178 = 0

using Newton-Raphson:

x \approx - 1.30813 \dots

Apply long division:

\frac{35 x ^{6} - 2 x - 178}{x + 1.30813 \dots} = 35 x^{5} - 45.78482 \dots x^{4} + 59.89287 \dots x^{3} - 78.34813 \dots x^{2} + 102.49016 \dots x - 136.07127 \dots

35 x^{5} - 45.78482 \dots x^{4} + 59.89287 \dots x^{3} - 78.34813 \dots x^{2} + 102.49016 \dots x - 136.07127 \dots \approx 0

Find one solution for

35 x^{5} - 45.78482 \dots x^{4} + 59.89287 \dots x^{3} - 78.34813 \dots x^{2} + 102.49016 \dots x - 136.07127 \dots = 0

using Newton-Raphson:

x \approx 1.31457 \dots

Apply long division:

\frac{35 x ^{5} - 45.78482 \dots x ^{4} + 59.89287 \dots x ^{3} - 78.34813 \dots x ^{2} + 102.49016 \dots x - 136.07127 \dots}{x - 1.31457 \dots} = 35 x^{4} + 0.22543 \dots x^{3} + 60.18921 \dots x^{2} + 0.77533 \dots x + 103.50940 \dots

35 x^{4} + 0.22543 \dots x^{3} + 60.18921 \dots x^{2} + 0.77533 \dots x + 103.50940 \dots \approx 0

Find one solution for

35 x^{4} + 0.22543 \dots x^{3} + 60.18921 \dots x^{2} + 0.77533 \dots x + 103.50940 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 1.30813 \dots, x \approx 1.31457 \dots

x^{5} - 3 x - 15 = 0

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

m^{4} - m^{2} = 0

x^{3} + 5 x - 774 = 0

4 x^{3} = 8

What are the solutions to the equation 2x=(35x^6)-178 ?
The solutions to the equation 2x=(35x^6)-178 are x\approx-1.30813…,x\approx 1.31457…
Find the zeros of 2x=(35x^6)-178
The zeros of 2x=(35x^6)-178 are x\approx-1.30813…,x\approx 1.31457…