What are the solutions to the equation 2a^3+0.5(4a+8)=9-2a ?

The solutions to the equation 2a^3+0.5(4a+8)=9-2a are a\approx 0.89342…

Find the zeros of 2a^3+0.5(4a+8)=9-2a

The zeros of 2a^3+0.5(4a+8)=9-2a are a\approx 0.89342…

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2 a^{3} + 0.5 (4 a + 8) = 9 - 2 a

a \approx 0.89342 \dots

Solution steps

2 a^{3} + 0.5 (4 a + 8) = 9 - 2 a

Multiply both sides by

10

20 a^{3} + 5 (4 a + 8) = 90 - 20 a

Expand

20 a^{3} + 5 (4 a + 8) : 20 a^{3} + 20 a + 40

20 a^{3} + 20 a + 40 = 90 - 20 a

Move

20 a

to the left side

20 a^{3} + 40 a + 40 = 90

Move

90

to the left side

20 a^{3} + 40 a - 50 = 0

Find one solution for

20 a^{3} + 40 a - 50 = 0

using Newton-Raphson:

a \approx 0.89342 \dots

Apply long division:

\frac{20 a ^{3} + 40 a - 50}{a - 0.89342 \dots} = 20 a^{2} + 17.86854 \dots a + 55.96425 \dots

20 a^{2} + 17.86854 \dots a + 55.96425 \dots \approx 0

Find one solution for

20 a^{2} + 17.86854 \dots a + 55.96425 \dots = 0

using Newton-Raphson:

No Solution for

a \in R

The solution is

a \approx 0.89342 \dots

0 = 2 x^{3}

1 - 2 x^{3} = 0

x^{3} + 6 x^{2} + 25 x + 150 = 0

y^{4} = y^{5}

(x - 1)^{3} = 16777216

What are the solutions to the equation 2a^3+0.5(4a+8)=9-2a ?
The solutions to the equation 2a^3+0.5(4a+8)=9-2a are a\approx 0.89342…
Find the zeros of 2a^3+0.5(4a+8)=9-2a
The zeros of 2a^3+0.5(4a+8)=9-2a are a\approx 0.89342…