What are the solutions to the equation 3x+2=2x^4 ?

The solutions to the equation 3x+2=2x^4 are x\approx-0.58733…,x\approx 1.31265…

Find the zeros of 3x+2=2x^4

The zeros of 3x+2=2x^4 are x\approx-0.58733…,x\approx 1.31265…

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3 x + 2 = 2 x^{4}

x \approx - 0.58733 \dots, x \approx 1.31265 \dots

Solution steps

3 x + 2 = 2 x^{4}

Switch sides

2 x^{4} = 3 x + 2

Move

2

to the left side

2 x^{4} - 2 = 3 x

Move

3 x

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.58733 \dots

Apply long division:

\frac{2 x ^{4} - 3 x - 2}{x + 0.58733 \dots} = 2 x^{3} - 1.17466 \dots x^{2} + 0.68992 \dots x - 3.40521 \dots

2 x^{3} - 1.17466 \dots x^{2} + 0.68992 \dots x - 3.40521 \dots \approx 0

Find one solution for

2 x^{3} - 1.17466 \dots x^{2} + 0.68992 \dots x - 3.40521 \dots = 0

using Newton-Raphson:

x \approx 1.31265 \dots

Apply long division:

\frac{2 x ^{3} - 1.17466 \dots x ^{2} + 0.68992 \dots x - 3.40521 \dots}{x - 1.31265 \dots} = 2 x^{2} + 1.45065 \dots x + 2.59413 \dots

2 x^{2} + 1.45065 \dots x + 2.59413 \dots \approx 0

Find one solution for

2 x^{2} + 1.45065 \dots x + 2.59413 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.58733 \dots, x \approx 1.31265 \dots

3 x^{3} + 12 x^{2} - 9 x - 15 = 0

x^{3} - 4 x^{2} - 29 x - 24 = 0

a^{3} + a^{2} - 3 = 0

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

x^{2} (x^{2} - 1) = 16 (x^{2} - 1)

What are the solutions to the equation 3x+2=2x^4 ?
The solutions to the equation 3x+2=2x^4 are x\approx-0.58733…,x\approx 1.31265…
Find the zeros of 3x+2=2x^4
The zeros of 3x+2=2x^4 are x\approx-0.58733…,x\approx 1.31265…