What are the solutions to the equation 10c^5c+16.5=13.5+10c ?

The solutions to the equation 10c^5c+16.5=13.5+10c are c\approx 0.30073…,c\approx 0.92454…

Find the zeros of 10c^5c+16.5=13.5+10c

The zeros of 10c^5c+16.5=13.5+10c are c\approx 0.30073…,c\approx 0.92454…

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10 c^{5} c + 16.5 = 13.5 + 10 c

c \approx 0.30073 \dots, c \approx 0.92454 \dots

Solution steps

10 c^{5} c + 16.5 = 13.5 + 10 c

Multiply both sides by

10

100 c^{6} + 165 = 135 + 100 c

Move

100 c

to the left side

100 c^{6} + 165 - 100 c = 135

Move

135

to the left side

100 c^{6} - 100 c + 30 = 0

Find one solution for

100 c^{6} - 100 c + 30 = 0

using Newton-Raphson:

c \approx 0.30073 \dots

Apply long division:

\frac{100 c ^{6} - 100 c + 30}{c - 0.30073 \dots} = 100 c^{5} + 30.07398 \dots c^{4} + 9.04444 \dots c^{3} + 2.72002 \dots c^{2} + 0.81802 \dots c - 99.75398 \dots

100 c^{5} + 30.07398 \dots c^{4} + 9.04444 \dots c^{3} + 2.72002 \dots c^{2} + 0.81802 \dots c - 99.75398 \dots \approx 0

Find one solution for

100 c^{5} + 30.07398 \dots c^{4} + 9.04444 \dots c^{3} + 2.72002 \dots c^{2} + 0.81802 \dots c - 99.75398 \dots = 0

using Newton-Raphson:

c \approx 0.92454 \dots

Apply long division:

\frac{100 c ^{5} + 30.07398 \dots c ^{4} + 9.04444 \dots c ^{3} + 2.72002 \dots c ^{2} + 0.81802 \dots c - 99.75398 \dots}{c - 0.92454 \dots} = 100 c^{4} + 122.52826 \dots c^{3} + 122.32707 \dots c^{2} + 115.81665 \dots c + 107.89547 \dots

100 c^{4} + 122.52826 \dots c^{3} + 122.32707 \dots c^{2} + 115.81665 \dots c + 107.89547 \dots \approx 0

Find one solution for

100 c^{4} + 122.52826 \dots c^{3} + 122.32707 \dots c^{2} + 115.81665 \dots c + 107.89547 \dots = 0

using Newton-Raphson:

No Solution for

c \in R

The solutions are

c \approx 0.30073 \dots, c \approx 0.92454 \dots

x^{3} - 6 x^{2} + 2 x + 24 = 0

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

x^{4} - 5 x^{6} = x + 1

1000000 = 100000 (x^{20})

x^{3} = \frac{64}{729}

What are the solutions to the equation 10c^5c+16.5=13.5+10c ?
The solutions to the equation 10c^5c+16.5=13.5+10c are c\approx 0.30073…,c\approx 0.92454…
Find the zeros of 10c^5c+16.5=13.5+10c
The zeros of 10c^5c+16.5=13.5+10c are c\approx 0.30073…,c\approx 0.92454…