What are the solutions to the equation 8x^4(x-1)=7 ?

The solutions to the equation 8x^4(x-1)=7 are x\approx 1.30328…

Find the zeros of 8x^4(x-1)=7

The zeros of 8x^4(x-1)=7 are x\approx 1.30328…

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8 x^{4} (x - 1) = 7

x \approx 1.30328 \dots

Solution steps

8 x^{4} (x - 1) = 7

Expand

8 x^{4} (x - 1) : 8 x^{5} - 8 x^{4}

8 x^{5} - 8 x^{4} = 7

Move

7

to the left side

8 x^{5} - 8 x^{4} - 7 = 0

Find one solution for

8 x^{5} - 8 x^{4} - 7 = 0

using Newton-Raphson:

x \approx 1.30328 \dots

Apply long division:

\frac{8 x ^{5} - 8 x ^{4} - 7}{x - 1.30328 \dots} = 8 x^{4} + 2.42627 \dots x^{3} + 3.16213 \dots x^{2} + 4.12115 \dots x + 5.37104 \dots

8 x^{4} + 2.42627 \dots x^{3} + 3.16213 \dots x^{2} + 4.12115 \dots x + 5.37104 \dots \approx 0

Find one solution for

8 x^{4} + 2.42627 \dots x^{3} + 3.16213 \dots x^{2} + 4.12115 \dots x + 5.37104 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.30328 \dots

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

0.037 = (1 + \frac{x}{12})^{12} - 1

14 x^{4} - 5 x^{2} - 1 = 0

x^{3} - 2 x^{2} - 5 x + 1 = 0

2 x^{3} - 54 = 0

What are the solutions to the equation 8x^4(x-1)=7 ?
The solutions to the equation 8x^4(x-1)=7 are x\approx 1.30328…
Find the zeros of 8x^4(x-1)=7
The zeros of 8x^4(x-1)=7 are x\approx 1.30328…