What are the solutions to the equation (3x-2)(x+1)^2(3x+8)=16 ?

The solutions to the equation (3x-2)(x+1)^2(3x+8)=16 are x\approx 0.82049…,x\approx-2.82049…

Find the zeros of (3x-2)(x+1)^2(3x+8)=16

The zeros of (3x-2)(x+1)^2(3x+8)=16 are x\approx 0.82049…,x\approx-2.82049…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(3 x - 2) (x + 1)^{2} (3 x + 8) = 16

x \approx 0.82049 \dots, x \approx - 2.82049 \dots

Solution steps

(3 x - 2) (x + 1)^{2} (3 x + 8) = 16

Expand

(3 x - 2) (x + 1)^{2} (3 x + 8) : 9 x^{4} + 36 x^{3} + 29 x^{2} - 14 x - 16

9 x^{4} + 36 x^{3} + 29 x^{2} - 14 x - 16 = 16

Move

16

to the left side

9 x^{4} + 36 x^{3} + 29 x^{2} - 14 x - 32 = 0

Find one solution for

9 x^{4} + 36 x^{3} + 29 x^{2} - 14 x - 32 = 0

using Newton-Raphson:

x \approx 0.82049 \dots

Apply long division:

\frac{9 x ^{4} + 36 x ^{3} + 29 x ^{2} - 14 x - 32}{x - 0.82049 \dots} = 9 x^{3} + 43.38442 \dots x^{2} + 64.59658 \dots x + 39.00098 \dots

9 x^{3} + 43.38442 \dots x^{2} + 64.59658 \dots x + 39.00098 \dots \approx 0

Find one solution for

9 x^{3} + 43.38442 \dots x^{2} + 64.59658 \dots x + 39.00098 \dots = 0

using Newton-Raphson:

x \approx - 2.82049 \dots

Apply long division:

\frac{9 x ^{3} + 43.38442 \dots x ^{2} + 64.59658 \dots x + 39.00098 \dots}{x + 2.82049 \dots} = 9 x^{2} + 18 x + 13.82772 \dots

9 x^{2} + 18 x + 13.82772 \dots \approx 0

Find one solution for

9 x^{2} + 18 x + 13.82772 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.82049 \dots, x \approx - 2.82049 \dots

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

(x^{2} + x) (x^{2} - x) = (x - 2)^{2} + x (x + 4)

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

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

x^{4} - 18 x^{2} + 81 = 0

What are the solutions to the equation (3x-2)(x+1)^2(3x+8)=16 ?
The solutions to the equation (3x-2)(x+1)^2(3x+8)=16 are x\approx 0.82049…,x\approx-2.82049…
Find the zeros of (3x-2)(x+1)^2(3x+8)=16
The zeros of (3x-2)(x+1)^2(3x+8)=16 are x\approx 0.82049…,x\approx-2.82049…