What are the solutions to the equation 8x-2=7x^9 ?

The solutions to the equation 8x-2=7x^9 are x\approx 0.25000…,x\approx 0.98008…,x\approx-1.04447…

Find the zeros of 8x-2=7x^9

The zeros of 8x-2=7x^9 are x\approx 0.25000…,x\approx 0.98008…,x\approx-1.04447…

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8 x - 2 = 7 x^{9}

x \approx 0.25000 \dots, x \approx 0.98008 \dots, x \approx - 1.04447 \dots

Solution steps

8 x - 2 = 7 x^{9}

Switch sides

7 x^{9} = 8 x - 2

Move

2

to the left side

7 x^{9} + 2 = 8 x

Move

8 x

to the left side

7 x^{9} + 2 - 8 x = 0

Write in the standard form

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

7 x^{9} - 8 x + 2 = 0

Find one solution for

7 x^{9} - 8 x + 2 = 0

using Newton-Raphson:

x \approx 0.25000 \dots

Apply long division:

\frac{7 x ^{9} - 8 x + 2}{x - 0.25000 \dots} = 7 x^{8} + 1.75002 \dots x^{7} + 0.43751 \dots x^{6} + 0.10937 \dots x^{5} + 0.02734 \dots x^{4} + 0.00683 \dots x^{3} + 0.00170 \dots x^{2} + 0.00042 \dots x - 7.99989 \dots

7 x^{8} + 1.75002 \dots x^{7} + 0.43751 \dots x^{6} + 0.10937 \dots x^{5} + 0.02734 \dots x^{4} + 0.00683 \dots x^{3} + 0.00170 \dots x^{2} + 0.00042 \dots x - 7.99989 \dots \approx 0

Find one solution for

7 x^{8} + 1.75002 \dots x^{7} + 0.43751 \dots x^{6} + 0.10937 \dots x^{5} + 0.02734 \dots x^{4} + 0.00683 \dots x^{3} + 0.00170 \dots x^{2} + 0.00042 \dots x - 7.99989 \dots = 0

using Newton-Raphson:

x \approx 0.98008 \dots

Apply long division:

\frac{7 x ^{8} + 1.75002 \dots x ^{7} + 0.43751 \dots x ^{6} + 0.10937 \dots x ^{5} + 0.02734 \dots x ^{4} + 0.00683 \dots x ^{3} + 0.00170 \dots x ^{2} + 0.00042 \dots x - 7.99989 \dots}{x - 0.98008 \dots} = 7 x^{7} + 8.61060 \dots x^{6} + 8.87661 \dots x^{5} + 8.80919 \dots x^{4} + 8.66108 \dots x^{3} + 8.49540 \dots x^{2} + 8.32791 \dots x + 8.16246 \dots

7 x^{7} + 8.61060 \dots x^{6} + 8.87661 \dots x^{5} + 8.80919 \dots x^{4} + 8.66108 \dots x^{3} + 8.49540 \dots x^{2} + 8.32791 \dots x + 8.16246 \dots \approx 0

Find one solution for

7 x^{7} + 8.61060 \dots x^{6} + 8.87661 \dots x^{5} + 8.80919 \dots x^{4} + 8.66108 \dots x^{3} + 8.49540 \dots x^{2} + 8.32791 \dots x + 8.16246 \dots = 0

using Newton-Raphson:

x \approx - 1.04447 \dots

Apply long division:

\frac{7 x ^{7} + 8.61060 \dots x ^{6} + 8.87661 \dots x ^{5} + 8.80919 \dots x ^{4} + 8.66108 \dots x ^{3} + 8.49540 \dots x ^{2} + 8.32791 \dots x + 8.16246 \dots}{x + 1.04447 \dots} = 7 x^{6} + 1.29926 \dots x^{5} + 7.51955 \dots x^{4} + 0.95519 \dots x^{3} + 7.66340 \dots x^{2} + 0.49117 \dots x + 7.81489 \dots

7 x^{6} + 1.29926 \dots x^{5} + 7.51955 \dots x^{4} + 0.95519 \dots x^{3} + 7.66340 \dots x^{2} + 0.49117 \dots x + 7.81489 \dots \approx 0

Find one solution for

7 x^{6} + 1.29926 \dots x^{5} + 7.51955 \dots x^{4} + 0.95519 \dots x^{3} + 7.66340 \dots x^{2} + 0.49117 \dots x + 7.81489 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.25000 \dots, x \approx 0.98008 \dots, x \approx - 1.04447 \dots

- 7 x^{2} - 8 + x^{4} = 0

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

6 x^{3} - x^{2} = 12 x

- 4 y^{3} + 300 y^{2} - 250000 = 0

16 x^{4} - 4 x^{2} + 1 = 0

What are the solutions to the equation 8x-2=7x^9 ?
The solutions to the equation 8x-2=7x^9 are x\approx 0.25000…,x\approx 0.98008…,x\approx-1.04447…
Find the zeros of 8x-2=7x^9
The zeros of 8x-2=7x^9 are x\approx 0.25000…,x\approx 0.98008…,x\approx-1.04447…