What are the solutions to the equation 8x^{12}=6x+4 ?

The solutions to the equation 8x^{12}=6x+4 are x\approx-0.65789…,x\approx 1.01977…

Find the zeros of 8x^{12}=6x+4

The zeros of 8x^{12}=6x+4 are x\approx-0.65789…,x\approx 1.01977…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

8 x^{12} = 6 x + 4

x \approx - 0.65789 \dots, x \approx 1.01977 \dots

Solution steps

8 x^{12} = 6 x + 4

Move

4

to the left side

8 x^{12} - 4 = 6 x

Move

6 x

to the left side

8 x^{12} - 4 - 6 x = 0

Write in the standard form

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

8 x^{12} - 6 x - 4 = 0

Find one solution for

8 x^{12} - 6 x - 4 = 0

using Newton-Raphson:

x \approx - 0.65789 \dots

Apply long division:

\frac{8 x ^{12} - 6 x - 4}{x + 0.65789 \dots} = 8 x^{11} - 5.26319 \dots x^{10} + 3.46265 \dots x^{9} - 2.27807 \dots x^{8} + 1.49874 \dots x^{7} - 0.98602 \dots x^{6} + 0.64870 \dots x^{5} - 0.42678 \dots x^{4} + 0.28078 \dots x^{3} - 0.18472 \dots x^{2} + 0.12153 \dots x - 6.07995 \dots

8 x^{11} - 5.26319 \dots x^{10} + 3.46265 \dots x^{9} - 2.27807 \dots x^{8} + 1.49874 \dots x^{7} - 0.98602 \dots x^{6} + 0.64870 \dots x^{5} - 0.42678 \dots x^{4} + 0.28078 \dots x^{3} - 0.18472 \dots x^{2} + 0.12153 \dots x - 6.07995 \dots \approx 0

Find one solution for

8 x^{11} - 5.26319 \dots x^{10} + 3.46265 \dots x^{9} - 2.27807 \dots x^{8} + 1.49874 \dots x^{7} - 0.98602 \dots x^{6} + 0.64870 \dots x^{5} - 0.42678 \dots x^{4} + 0.28078 \dots x^{3} - 0.18472 \dots x^{2} + 0.12153 \dots x - 6.07995 \dots = 0

using Newton-Raphson:

x \approx 1.01977 \dots

Apply long division:

\frac{8 x ^{11} - 5.26319 \dots x ^{10} + 3.46265 \dots x ^{9} - 2.27807 \dots x ^{8} + 1.49874 \dots x ^{7} - 0.98602 \dots x ^{6} + 0.64870 \dots x ^{5} - 0.42678 \dots x ^{4} + 0.28078 \dots x ^{3} - 0.18472 \dots x ^{2} + 0.12153 \dots x - 6.07995 \dots}{x - 1.01977 \dots} = 8 x^{10} + 2.89497 \dots x^{9} + 6.41486 \dots x^{8} + 4.26361 \dots x^{7} + 5.84665 \dots x^{6} + 4.97622 \dots x^{5} + 5.72331 \dots x^{4} + 5.40968 \dots x^{3} + 5.79741 \dots x^{2} + 5.72731 \dots x + 5.96207 \dots

8 x^{10} + 2.89497 \dots x^{9} + 6.41486 \dots x^{8} + 4.26361 \dots x^{7} + 5.84665 \dots x^{6} + 4.97622 \dots x^{5} + 5.72331 \dots x^{4} + 5.40968 \dots x^{3} + 5.79741 \dots x^{2} + 5.72731 \dots x + 5.96207 \dots \approx 0

Find one solution for

8 x^{10} + 2.89497 \dots x^{9} + 6.41486 \dots x^{8} + 4.26361 \dots x^{7} + 5.84665 \dots x^{6} + 4.97622 \dots x^{5} + 5.72331 \dots x^{4} + 5.40968 \dots x^{3} + 5.79741 \dots x^{2} + 5.72731 \dots x + 5.96207 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.65789 \dots, x \approx 1.01977 \dots

2 x - 712 - 4 - x^{6} = 1920

(7 x + 1) (5 x^{3} - 10 x^{2}) = 0

(x^{2} - 5 x) (x - 36) = 0

(2 x^{3}) x^{8} = 2 x (3 x^{8})

x = - (x - 3)^{3}

What are the solutions to the equation 8x^{12}=6x+4 ?
The solutions to the equation 8x^{12}=6x+4 are x\approx-0.65789…,x\approx 1.01977…
Find the zeros of 8x^{12}=6x+4
The zeros of 8x^{12}=6x+4 are x\approx-0.65789…,x\approx 1.01977…