What are the solutions to the equation a^3+12a-6.5=0 ?

The solutions to the equation a^3+12a-6.5=0 are a\approx 0.52930…

Find the zeros of a^3+12a-6.5=0

The zeros of a^3+12a-6.5=0 are a\approx 0.52930…

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a^{3} + 12 a - 6.5 = 0

a \approx 0.52930 \dots

Solution steps

a^{3} + 12 a - 6.5 = 0

Multiply both sides by

10

10 a^{3} + 120 a - 65 = 0

Find one solution for

10 a^{3} + 120 a - 65 = 0

using Newton-Raphson:

a \approx 0.52930 \dots

Apply long division:

\frac{10 a ^{3} + 120 a - 65}{a - 0.52930 \dots} = 10 a^{2} + 5.29308 \dots a + 122.80167 \dots

10 a^{2} + 5.29308 \dots a + 122.80167 \dots \approx 0

Find one solution for

10 a^{2} + 5.29308 \dots a + 122.80167 \dots = 0

using Newton-Raphson:

No Solution for

a \in R

The solution is

a \approx 0.52930 \dots

8 (1.2 - x^{2})^{2} = 0.5 x^{2}

76 = \frac{1}{2} (h (h^{2} + 3))

x^{2} = 8 x^{15}

4 x^{3} - 6 x^{2} - 20 x + 30 = 0

(x^{2} - 8 x + 15) (x + 1) = 0

What are the solutions to the equation a^3+12a-6.5=0 ?
The solutions to the equation a^3+12a-6.5=0 are a\approx 0.52930…
Find the zeros of a^3+12a-6.5=0
The zeros of a^3+12a-6.5=0 are a\approx 0.52930…