What are the solutions to the equation (x)=(x^3+8)*(3x-15) ?

The solutions to the equation (x)=(x^3+8)*(3x-15) are x\approx 5.01247…,x\approx-1.99205…

Find the zeros of (x)=(x^3+8)*(3x-15)

The zeros of (x)=(x^3+8)*(3x-15) are x\approx 5.01247…,x\approx-1.99205…

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(x) = (x^{3} + 8) \cdot (3 x - 15)

x \approx 5.01247 \dots, x \approx - 1.99205 \dots

Solution steps

(x) = (x^{3} + 8) (3 x - 15)

Expand

(x^{3} + 8) (3 x - 15) : 3 x^{4} - 15 x^{3} + 24 x - 120

x = 3 x^{4} - 15 x^{3} + 24 x - 120

Switch sides

3 x^{4} - 15 x^{3} + 24 x - 120 = x

Move

x

to the left side

3 x^{4} - 15 x^{3} + 23 x - 120 = 0

Find one solution for

3 x^{4} - 15 x^{3} + 23 x - 120 = 0

using Newton-Raphson:

x \approx 5.01247 \dots

Apply long division:

\frac{3 x ^{4} - 15 x ^{3} + 23 x - 120}{x - 5.01247 \dots} = 3 x^{3} + 0.03742 \dots x^{2} + 0.18758 \dots x + 23.94027 \dots

3 x^{3} + 0.03742 \dots x^{2} + 0.18758 \dots x + 23.94027 \dots \approx 0

Find one solution for

3 x^{3} + 0.03742 \dots x^{2} + 0.18758 \dots x + 23.94027 \dots = 0

using Newton-Raphson:

x \approx - 1.99205 \dots

Apply long division:

\frac{3 x ^{3} + 0.03742 \dots x ^{2} + 0.18758 \dots x + 23.94027 \dots}{x + 1.99205 \dots} = 3 x^{2} - 5.93873 \dots x + 12.01787 \dots

3 x^{2} - 5.93873 \dots x + 12.01787 \dots \approx 0

Find one solution for

3 x^{2} - 5.93873 \dots x + 12.01787 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 5.01247 \dots, x \approx - 1.99205 \dots

(x + 1)^{5} = \frac{1}{32}

(x + 2)^{2} \cdot (x + 6)^{3} + (x + 2) \cdot (x + 6)^{4} = 0

x^{6} = 5

(3 x - 2) (x^{1}) - (2 x^{3}) (2 - x) = 182 x

(x^{2} - 3 x)^{2} - 16 (x^{2} - 3 x) - 36 = 0

What are the solutions to the equation (x)=(x^3+8)*(3x-15) ?
The solutions to the equation (x)=(x^3+8)*(3x-15) are x\approx 5.01247…,x\approx-1.99205…
Find the zeros of (x)=(x^3+8)*(3x-15)
The zeros of (x)=(x^3+8)*(3x-15) are x\approx 5.01247…,x\approx-1.99205…