What are the solutions to the equation 2x^5+36=2x-6 ?

The solutions to the equation 2x^5+36=2x-6 are x\approx-1.87005…

Find the zeros of 2x^5+36=2x-6

The zeros of 2x^5+36=2x-6 are x\approx-1.87005…

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2 x^{5} + 36 = 2 x - 6

x \approx - 1.87005 \dots

Solution steps

2 x^{5} + 36 = 2 x - 6

Move

6

to the left side

2 x^{5} + 42 = 2 x

Move

2 x

to the left side

2 x^{5} + 42 - 2 x = 0

Write in the standard form

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

2 x^{5} - 2 x + 42 = 0

Find one solution for

2 x^{5} - 2 x + 42 = 0

using Newton-Raphson:

x \approx - 1.87005 \dots

Apply long division:

\frac{2 x ^{5} - 2 x + 42}{x + 1.87005 \dots} = 2 x^{4} - 3.74010 \dots x^{3} + 6.99418 \dots x^{2} - 13.07947 \dots x + 22.45928 \dots

2 x^{4} - 3.74010 \dots x^{3} + 6.99418 \dots x^{2} - 13.07947 \dots x + 22.45928 \dots \approx 0

Find one solution for

2 x^{4} - 3.74010 \dots x^{3} + 6.99418 \dots x^{2} - 13.07947 \dots x + 22.45928 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.87005 \dots

4 x^{4} - 8 x^{2} + 3 = 0

x^{4} = 41

(x^{2} - 1) \cdot (x^{2} - 12) + 24 = 0

x^{10} = 263

a^{3} + (- b^{2}) = x^{3} + 1

What are the solutions to the equation 2x^5+36=2x-6 ?
The solutions to the equation 2x^5+36=2x-6 are x\approx-1.87005…
Find the zeros of 2x^5+36=2x-6
The zeros of 2x^5+36=2x-6 are x\approx-1.87005…