What are the solutions to the equation v^8v+4v-14=-53 ?

The solutions to the equation v^8v+4v-14=-53 are v\approx-1.47525…

Find the zeros of v^8v+4v-14=-53

The zeros of v^8v+4v-14=-53 are v\approx-1.47525…

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v^{8} v + 4 v - 14 = - 53

v \approx - 1.47525 \dots

Solution steps

v^{8} v + 4 v - 14 = - 53

Expand

v^{8} v + 4 v - 14 : v^{9} + 4 v - 14

v^{9} + 4 v - 14 = - 53

Move

53

to the left side

v^{9} + 4 v + 39 = 0

Find one solution for

v^{9} + 4 v + 39 = 0

using Newton-Raphson:

v \approx - 1.47525 \dots

Apply long division:

\frac{v ^{9} + 4 v + 39}{v + 1.47525 \dots} = v^{8} - 1.47525 \dots v^{7} + 2.17638 \dots v^{6} - 3.21073 \dots v^{5} + 4.73666 \dots v^{4} - 6.98781 \dots v^{3} + 10.30883 \dots v^{2} - 15.20820 \dots v + 26.43603 \dots

v^{8} - 1.47525 \dots v^{7} + 2.17638 \dots v^{6} - 3.21073 \dots v^{5} + 4.73666 \dots v^{4} - 6.98781 \dots v^{3} + 10.30883 \dots v^{2} - 15.20820 \dots v + 26.43603 \dots \approx 0

Find one solution for

v^{8} - 1.47525 \dots v^{7} + 2.17638 \dots v^{6} - 3.21073 \dots v^{5} + 4.73666 \dots v^{4} - 6.98781 \dots v^{3} + 10.30883 \dots v^{2} - 15.20820 \dots v + 26.43603 \dots = 0

using Newton-Raphson:

No Solution for

v \in R

The solution is

v \approx - 1.47525 \dots

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

2 x^{3} + 16 x^{2} + 30 x = 0

x^{6} - x^{3} - 6 = 0

y^{4} + 4 y^{2} - 5 = 0

0.25 = e^{4}

What are the solutions to the equation v^8v+4v-14=-53 ?
The solutions to the equation v^8v+4v-14=-53 are v\approx-1.47525…
Find the zeros of v^8v+4v-14=-53
The zeros of v^8v+4v-14=-53 are v\approx-1.47525…