What are the solutions to the equation x^4+2x^3=7 ?

The solutions to the equation x^4+2x^3=7 are x\approx 1.28661…,x\approx-2.46650…

Find the zeros of x^4+2x^3=7

The zeros of x^4+2x^3=7 are x\approx 1.28661…,x\approx-2.46650…

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x^{4} + 2 x^{3} = 7

x \approx 1.28661 \dots, x \approx - 2.46650 \dots

Solution steps

x^{4} + 2 x^{3} = 7

Move

7

to the left side

x^{4} + 2 x^{3} - 7 = 0

Find one solution for

x^{4} + 2 x^{3} - 7 = 0

using Newton-Raphson:

x \approx 1.28661 \dots

Apply long division:

\frac{x ^{4} + 2 x ^{3} - 7}{x - 1.28661 \dots} = x^{3} + 3.28661 \dots x^{2} + 4.22862 \dots x + 5.44062 \dots

x^{3} + 3.28661 \dots x^{2} + 4.22862 \dots x + 5.44062 \dots \approx 0

Find one solution for

x^{3} + 3.28661 \dots x^{2} + 4.22862 \dots x + 5.44062 \dots = 0

using Newton-Raphson:

x \approx - 2.46650 \dots

Apply long division:

\frac{x ^{3} + 3.28661 \dots x ^{2} + 4.22862 \dots x + 5.44062 \dots}{x + 2.46650 \dots} = x^{2} + 0.82011 \dots x + 2.20580 \dots

x^{2} + 0.82011 \dots x + 2.20580 \dots \approx 0

Find one solution for

x^{2} + 0.82011 \dots x + 2.20580 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.28661 \dots, x \approx - 2.46650 \dots

4 x^{3} - 36 x^{2} - 84 x = 0

x^{3} - 3 x + 2

4 x^{3} - 12 x^{2} - 11 x - 2 = 0

x^{5} = 64 x^{2}

- 16 x - 4 x^{3} = 164

What are the solutions to the equation x^4+2x^3=7 ?
The solutions to the equation x^4+2x^3=7 are x\approx 1.28661…,x\approx-2.46650…
Find the zeros of x^4+2x^3=7
The zeros of x^4+2x^3=7 are x\approx 1.28661…,x\approx-2.46650…