What are the solutions to the equation 5-x^3=x^2+6 ?

The solutions to the equation 5-x^3=x^2+6 are x\approx-1.46557…

Find the zeros of 5-x^3=x^2+6

The zeros of 5-x^3=x^2+6 are x\approx-1.46557…

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

x \approx - 1.46557 \dots

Solution steps

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

Move

6

to the left side

- x^{3} - 1 = x^{2}

Move

x^{2}

to the left side

- x^{3} - 1 - x^{2} = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- x^{3} - x^{2} - 1 = 0

Find one solution for

- x^{3} - x^{2} - 1 = 0

using Newton-Raphson:

x \approx - 1.46557 \dots

Apply long division:

\frac{- x ^{3} - x ^{2} - 1}{x + 1.46557 \dots} = - x^{2} + 0.46557 \dots x - 0.68232 \dots

- x^{2} + 0.46557 \dots x - 0.68232 \dots \approx 0

Find one solution for

- x^{2} + 0.46557 \dots x - 0.68232 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.46557 \dots

9 x^{3} - 54 x^{2} - x + 6 = 0

23.92 x^{3} + 66.53 x^{2} - 300 = 0

z^{4} + 7 z^{2} - 144 = 0

3 x^{5} + 27 x^{3} = 0

x^{3} + 6 x^{2} + 9 x = - 3

What are the solutions to the equation 5-x^3=x^2+6 ?
The solutions to the equation 5-x^3=x^2+6 are x\approx-1.46557…
Find the zeros of 5-x^3=x^2+6
The zeros of 5-x^3=x^2+6 are x\approx-1.46557…