What are the solutions to the equation 4x^4+x-3=5x^5+x-6 ?

The solutions to the equation 4x^4+x-3=5x^5+x-6 are x\approx 1.14684…

Find the zeros of 4x^4+x-3=5x^5+x-6

The zeros of 4x^4+x-3=5x^5+x-6 are x\approx 1.14684…

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4 x^{4} + x - 3 = 5 x^{5} + x - 6

x \approx 1.14684 \dots

Solution steps

4 x^{4} + x - 3 = 5 x^{5} + x - 6

Switch sides

5 x^{5} + x - 6 = 4 x^{4} + x - 3

Move

3

to the left side

5 x^{5} + x - 3 = 4 x^{4} + x

Move

x

to the left side

5 x^{5} - 3 = 4 x^{4}

Move

4 x^{4}

to the left side

5 x^{5} - 3 - 4 x^{4} = 0

Write in the standard form

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

5 x^{5} - 4 x^{4} - 3 = 0

Find one solution for

5 x^{5} - 4 x^{4} - 3 = 0

using Newton-Raphson:

x \approx 1.14684 \dots

Apply long division:

\frac{5 x ^{5} - 4 x ^{4} - 3}{x - 1.14684 \dots} = 5 x^{4} + 1.73421 \dots x^{3} + 1.98887 \dots x^{2} + 2.28093 \dots x + 2.61587 \dots

5 x^{4} + 1.73421 \dots x^{3} + 1.98887 \dots x^{2} + 2.28093 \dots x + 2.61587 \dots \approx 0

Find one solution for

5 x^{4} + 1.73421 \dots x^{3} + 1.98887 \dots x^{2} + 2.28093 \dots x + 2.61587 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.14684 \dots

4 x + 8 = 6 x^{5} - 4

x^{4} - 4 x^{2} + 32 = 0

(d^{2} + 1)^{3} = 0

(x + 5)^{3} = \frac{- 64}{125}

n (n^{2} + 1) = 336

What are the solutions to the equation 4x^4+x-3=5x^5+x-6 ?
The solutions to the equation 4x^4+x-3=5x^5+x-6 are x\approx 1.14684…
Find the zeros of 4x^4+x-3=5x^5+x-6
The zeros of 4x^4+x-3=5x^5+x-6 are x\approx 1.14684…