What are the solutions to the equation -(-10x+1)-4x=7x^7x ?

The solutions to the equation -(-10x+1)-4x=7x^7x are x\approx 0.16666…,x\approx 0.95168…

Find the zeros of -(-10x+1)-4x=7x^7x

The zeros of -(-10x+1)-4x=7x^7x are x\approx 0.16666…,x\approx 0.95168…

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- (- 10 x + 1) - 4 x = 7 x^{7} x

x \approx 0.16666 \dots, x \approx 0.95168 \dots

Solution steps

- (- 10 x + 1) - 4 x = 7 x^{7} x

Expand

- (- 10 x + 1) - 4 x : 6 x - 1

Expand

7 x^{7} x : 7 x^{8}

6 x - 1 = 7 x^{8}

Switch sides

7 x^{8} = 6 x - 1

Move

1

to the left side

7 x^{8} + 1 = 6 x

Move

6 x

to the left side

7 x^{8} + 1 - 6 x = 0

Write in the standard form

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

7 x^{8} - 6 x + 1 = 0

Find one solution for

7 x^{8} - 6 x + 1 = 0

using Newton-Raphson:

x \approx 0.16666 \dots

Apply long division:

\frac{7 x ^{8} - 6 x + 1}{x - 0.16666 \dots} = 7 x^{7} + 1.16667 \dots x^{6} + 0.19444 \dots x^{5} + 0.03240 \dots x^{4} + 0.00540 \dots x^{3} + 0.00090 \dots x^{2} + 0.00015 \dots x - 5.99997 \dots

7 x^{7} + 1.16667 \dots x^{6} + 0.19444 \dots x^{5} + 0.03240 \dots x^{4} + 0.00540 \dots x^{3} + 0.00090 \dots x^{2} + 0.00015 \dots x - 5.99997 \dots \approx 0

Find one solution for

7 x^{7} + 1.16667 \dots x^{6} + 0.19444 \dots x^{5} + 0.03240 \dots x^{4} + 0.00540 \dots x^{3} + 0.00090 \dots x^{2} + 0.00015 \dots x - 5.99997 \dots = 0

using Newton-Raphson:

x \approx 0.95168 \dots

Apply long division:

\frac{7 x ^{7} + 1.16667 \dots x ^{6} + 0.19444 \dots x ^{5} + 0.03240 \dots x ^{4} + 0.00540 \dots x ^{3} + 0.00090 \dots x ^{2} + 0.00015 \dots x - 5.99997 \dots}{x - 0.95168 \dots} = 7 x^{6} + 7.82843 \dots x^{5} + 7.64462 \dots x^{4} + 7.30764 \dots x^{3} + 6.95994 \dots x^{2} + 6.62455 \dots x + 6.30460 \dots

7 x^{6} + 7.82843 \dots x^{5} + 7.64462 \dots x^{4} + 7.30764 \dots x^{3} + 6.95994 \dots x^{2} + 6.62455 \dots x + 6.30460 \dots \approx 0

Find one solution for

7 x^{6} + 7.82843 \dots x^{5} + 7.64462 \dots x^{4} + 7.30764 \dots x^{3} + 6.95994 \dots x^{2} + 6.62455 \dots x + 6.30460 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.16666 \dots, x \approx 0.95168 \dots

4 x^{3} + 4 x^{2} - 25 x - 25 = 0

- x^{3} + 8 x^{2} - 19 x + 12 = 0

x^{8} + 1 = 0

(x - 15)^{6} + 2 (15 - x)^{2} = 0

- x^{3} + 11 x^{2} - 39 x + 45 = 0

What are the solutions to the equation -(-10x+1)-4x=7x^7x ?
The solutions to the equation -(-10x+1)-4x=7x^7x are x\approx 0.16666…,x\approx 0.95168…
Find the zeros of -(-10x+1)-4x=7x^7x
The zeros of -(-10x+1)-4x=7x^7x are x\approx 0.16666…,x\approx 0.95168…