What are the solutions to the equation (8x-9)^3x=10 ?

The solutions to the equation (8x-9)^3x=10 are x\approx-0.01324…,x\approx 1.36761…

Find the zeros of (8x-9)^3x=10

The zeros of (8x-9)^3x=10 are x\approx-0.01324…,x\approx 1.36761…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(8 x - 9)^{3} x = 10

x \approx - 0.01324 \dots, x \approx 1.36761 \dots

Solution steps

(8 x - 9)^{3} x = 10

Expand

(8 x - 9)^{3} x : 512 x^{4} - 1728 x^{3} + 1944 x^{2} - 729 x

512 x^{4} - 1728 x^{3} + 1944 x^{2} - 729 x = 10

Move

10

to the left side

512 x^{4} - 1728 x^{3} + 1944 x^{2} - 729 x - 10 = 0

Find one solution for

512 x^{4} - 1728 x^{3} + 1944 x^{2} - 729 x - 10 = 0

using Newton-Raphson:

x \approx - 0.01324 \dots

Apply long division:

\frac{512 x ^{4} - 1728 x ^{3} + 1944 x ^{2} - 729 x - 10}{x + 0.01324 \dots} = 512 x^{3} - 1734.78099 \dots x^{2} + 1966.97568 \dots x - 755.05090 \dots

512 x^{3} - 1734.78099 \dots x^{2} + 1966.97568 \dots x - 755.05090 \dots \approx 0

Find one solution for

512 x^{3} - 1734.78099 \dots x^{2} + 1966.97568 \dots x - 755.05090 \dots = 0

using Newton-Raphson:

x \approx 1.36761 \dots

Apply long division:

\frac{512 x ^{3} - 1734.78099 \dots x ^{2} + 1966.97568 \dots x - 755.05090 \dots}{x - 1.36761 \dots} = 512 x^{2} - 1034.56092 \dots x + 552.09223 \dots

512 x^{2} - 1034.56092 \dots x + 552.09223 \dots \approx 0

Find one solution for

512 x^{2} - 1034.56092 \dots x + 552.09223 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.01324 \dots, x \approx 1.36761 \dots

45 x^{44} = 179

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

4 x^{3} + 23 x^{2} - 2 x = 0

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

4 x^{4} - 33 x^{2} + 50 = 0

What are the solutions to the equation (8x-9)^3x=10 ?
The solutions to the equation (8x-9)^3x=10 are x\approx-0.01324…,x\approx 1.36761…
Find the zeros of (8x-9)^3x=10
The zeros of (8x-9)^3x=10 are x\approx-0.01324…,x\approx 1.36761…