What are the solutions to the equation v^5v-12=4+32v ?

The solutions to the equation v^5v-12=4+32v are v\approx-0.49951…,v\approx 2.08775…

Find the zeros of v^5v-12=4+32v

The zeros of v^5v-12=4+32v are v\approx-0.49951…,v\approx 2.08775…

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v^{5} v - 12 = 4 + 32 v

v \approx - 0.49951 \dots, v \approx 2.08775 \dots

Solution steps

v^{5} v - 12 = 4 + 32 v

Expand

v^{5} v - 12 : v^{6} - 12

v^{6} - 12 = 4 + 32 v

Move

32 v

to the left side

v^{6} - 12 - 32 v = 4

Move

4

to the left side

v^{6} - 32 v - 16 = 0

Find one solution for

v^{6} - 32 v - 16 = 0

using Newton-Raphson:

v \approx - 0.49951 \dots

Apply long division:

\frac{v ^{6} - 32 v - 16}{v + 0.49951 \dots} = v^{5} - 0.49951 \dots v^{4} + 0.24951 \dots v^{3} - 0.12463 \dots v^{2} + 0.06225 \dots v - 32.03109 \dots

v^{5} - 0.49951 \dots v^{4} + 0.24951 \dots v^{3} - 0.12463 \dots v^{2} + 0.06225 \dots v - 32.03109 \dots \approx 0

Find one solution for

v^{5} - 0.49951 \dots v^{4} + 0.24951 \dots v^{3} - 0.12463 \dots v^{2} + 0.06225 \dots v - 32.03109 \dots = 0

using Newton-Raphson:

v \approx 2.08775 \dots

Apply long division:

\frac{v ^{5} - 0.49951 \dots v ^{4} + 0.24951 \dots v ^{3} - 0.12463 \dots v ^{2} + 0.06225 \dots v - 32.03109 \dots}{v - 2.08775 \dots} = v^{4} + 1.58823 \dots v^{3} + 3.56535 \dots v^{2} + 7.31894 \dots v + 15.34239 \dots

v^{4} + 1.58823 \dots v^{3} + 3.56535 \dots v^{2} + 7.31894 \dots v + 15.34239 \dots \approx 0

Find one solution for

v^{4} + 1.58823 \dots v^{3} + 3.56535 \dots v^{2} + 7.31894 \dots v + 15.34239 \dots = 0

using Newton-Raphson:

No Solution for

v \in R

The solutions are

v \approx - 0.49951 \dots, v \approx 2.08775 \dots

x^{3} + 10 = 45

x^{2} (x^{2} + 4) (x^{2} + 16) = 100

- x^{3} + 4 x^{2} + 7 x - 10 = 0

- x^{3} + 19 x - 30 = 0

6 x^{3} - 5 x^{2} - 2 x + 1 = 0

What are the solutions to the equation v^5v-12=4+32v ?
The solutions to the equation v^5v-12=4+32v are v\approx-0.49951…,v\approx 2.08775…
Find the zeros of v^5v-12=4+32v
The zeros of v^5v-12=4+32v are v\approx-0.49951…,v\approx 2.08775…