What are the solutions to the equation -0.024=x^4-2*x^5-x^6 ?

The solutions to the equation -0.024=x^4-2*x^5-x^6 are x\approx 0.52322…,x\approx-2.41446…

Find the zeros of -0.024=x^4-2*x^5-x^6

The zeros of -0.024=x^4-2*x^5-x^6 are x\approx 0.52322…,x\approx-2.41446…

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- 0.024 = x^{4} - 2 \cdot x^{5} - x^{6}

x \approx 0.52322 \dots, x \approx - 2.41446 \dots

Solution steps

- 0.024 = x^{4} - 2 x^{5} - x^{6}

Multiply both sides by

1000

- 24 = 1000 x^{4} - 2000 x^{5} - 1000 x^{6}

Switch sides

1000 x^{4} - 2000 x^{5} - 1000 x^{6} = - 24

Move

24

to the left side

1000 x^{4} - 2000 x^{5} - 1000 x^{6} + 24 = 0

Write in the standard form

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

- 1000 x^{6} - 2000 x^{5} + 1000 x^{4} + 24 = 0

Find one solution for

- 1000 x^{6} - 2000 x^{5} + 1000 x^{4} + 24 = 0

using Newton-Raphson:

x \approx 0.52322 \dots

Apply long division:

\frac{- 1000 x ^{6} - 2000 x ^{5} + 1000 x ^{4} + 24}{x - 0.52322 \dots} = - 1000 x^{5} - 2523.22720 \dots x^{4} - 320.22111 \dots x^{3} - 167.54840 \dots x^{2} - 87.66588 \dots x - 45.86917 \dots

- 1000 x^{5} - 2523.22720 \dots x^{4} - 320.22111 \dots x^{3} - 167.54840 \dots x^{2} - 87.66588 \dots x - 45.86917 \dots \approx 0

Find one solution for

- 1000 x^{5} - 2523.22720 \dots x^{4} - 320.22111 \dots x^{3} - 167.54840 \dots x^{2} - 87.66588 \dots x - 45.86917 \dots = 0

using Newton-Raphson:

x \approx - 2.41446 \dots

Apply long division:

\frac{- 1000 x ^{5} - 2523.22720 \dots x ^{4} - 320.22111 \dots x ^{3} - 167.54840 \dots x ^{2} - 87.66588 \dots x - 45.86917 \dots}{x + 2.41446 \dots} = - 1000 x^{4} - 108.76398 \dots x^{3} - 57.61447 \dots x^{2} - 28.44036 \dots x - 18.99766 \dots

- 1000 x^{4} - 108.76398 \dots x^{3} - 57.61447 \dots x^{2} - 28.44036 \dots x - 18.99766 \dots \approx 0

Find one solution for

- 1000 x^{4} - 108.76398 \dots x^{3} - 57.61447 \dots x^{2} - 28.44036 \dots x - 18.99766 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.52322 \dots, x \approx - 2.41446 \dots

z^{4} - 2 z^{3} + 5 z^{2} - 6 z + 6 = 0

m^{3} - m^{2} + 2 m - 2 = 0

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

t^{3} = - 1

2 x^{3} - 2 = 0

What are the solutions to the equation -0.024=x^4-2*x^5-x^6 ?
The solutions to the equation -0.024=x^4-2*x^5-x^6 are x\approx 0.52322…,x\approx-2.41446…
Find the zeros of -0.024=x^4-2*x^5-x^6
The zeros of -0.024=x^4-2*x^5-x^6 are x\approx 0.52322…,x\approx-2.41446…