What are the solutions to the equation 8x^7-7x^8=0.75 ?

The solutions to the equation 8x^7-7x^8=0.75 are x\approx 1.08057…,x\approx 0.87937…

Find the zeros of 8x^7-7x^8=0.75

The zeros of 8x^7-7x^8=0.75 are x\approx 1.08057…,x\approx 0.87937…

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8 x^{7} - 7 x^{8} = 0.75

x \approx 1.08057 \dots, x \approx 0.87937 \dots

Solution steps

8 x^{7} - 7 x^{8} = 0.75

Multiply both sides by

100

800 x^{7} - 700 x^{8} = 75

Move

75

to the left side

800 x^{7} - 700 x^{8} - 75 = 0

Write in the standard form

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

- 700 x^{8} + 800 x^{7} - 75 = 0

Find one solution for

- 700 x^{8} + 800 x^{7} - 75 = 0

using Newton-Raphson:

x \approx 1.08057 \dots

Apply long division:

\frac{- 700 x ^{8} + 800 x ^{7} - 75}{x - 1.08057 \dots} = - 700 x^{7} + 43.60006 \dots x^{6} + 47.11298 \dots x^{5} + 50.90894 \dots x^{4} + 55.01074 \dots x^{3} + 59.44303 \dots x^{2} + 64.23243 \dots x + 69.40772 \dots

- 700 x^{7} + 43.60006 \dots x^{6} + 47.11298 \dots x^{5} + 50.90894 \dots x^{4} + 55.01074 \dots x^{3} + 59.44303 \dots x^{2} + 64.23243 \dots x + 69.40772 \dots \approx 0

Find one solution for

- 700 x^{7} + 43.60006 \dots x^{6} + 47.11298 \dots x^{5} + 50.90894 \dots x^{4} + 55.01074 \dots x^{3} + 59.44303 \dots x^{2} + 64.23243 \dots x + 69.40772 \dots = 0

using Newton-Raphson:

x \approx 0.87937 \dots

Apply long division:

\frac{- 700 x ^{7} + 43.60006 \dots x ^{6} + 47.11298 \dots x ^{5} + 50.90894 \dots x ^{4} + 55.01074 \dots x ^{3} + 59.44303 \dots x ^{2} + 64.23243 \dots x + 69.40772 \dots}{x - 0.87937 \dots} = - 700 x^{6} - 571.95981 \dots x^{5} - 455.85203 \dots x^{4} - 349.95423 \dots x^{3} - 252.72895 \dots x^{2} - 162.79954 \dots x - 78.92881 \dots

- 700 x^{6} - 571.95981 \dots x^{5} - 455.85203 \dots x^{4} - 349.95423 \dots x^{3} - 252.72895 \dots x^{2} - 162.79954 \dots x - 78.92881 \dots \approx 0

Find one solution for

- 700 x^{6} - 571.95981 \dots x^{5} - 455.85203 \dots x^{4} - 349.95423 \dots x^{3} - 252.72895 \dots x^{2} - 162.79954 \dots x - 78.92881 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.08057 \dots, x \approx 0.87937 \dots

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

(8 + x)^{3} = 64

0 = 2 x^{(3)} + x^{(2)} + 2 x - 1

m^{3} = 125

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

What are the solutions to the equation 8x^7-7x^8=0.75 ?
The solutions to the equation 8x^7-7x^8=0.75 are x\approx 1.08057…,x\approx 0.87937…
Find the zeros of 8x^7-7x^8=0.75
The zeros of 8x^7-7x^8=0.75 are x\approx 1.08057…,x\approx 0.87937…