What are the solutions to the equation 2x-13=-x^4+6 ?

The solutions to the equation 2x-13=-x^4+6 are x\approx 1.96995…,x\approx-2.19936…

Find the zeros of 2x-13=-x^4+6

The zeros of 2x-13=-x^4+6 are x\approx 1.96995…,x\approx-2.19936…

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2 x - 13 = - x^{4} + 6

x \approx 1.96995 \dots, x \approx - 2.19936 \dots

Solution steps

2 x - 13 = - x^{4} + 6

Switch sides

- x^{4} + 6 = 2 x - 13

Move

13

to the left side

- x^{4} + 19 = 2 x

Move

2 x

to the left side

- x^{4} + 19 - 2 x = 0

Write in the standard form

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

- x^{4} - 2 x + 19 = 0

Find one solution for

- x^{4} - 2 x + 19 = 0

using Newton-Raphson:

x \approx 1.96995 \dots

Apply long division:

\frac{- x ^{4} - 2 x + 19}{x - 1.96995 \dots} = - x^{3} - 1.96995 \dots x^{2} - 3.88073 \dots x - 9.64487 \dots

- x^{3} - 1.96995 \dots x^{2} - 3.88073 \dots x - 9.64487 \dots \approx 0

Find one solution for

- x^{3} - 1.96995 \dots x^{2} - 3.88073 \dots x - 9.64487 \dots = 0

using Newton-Raphson:

x \approx - 2.19936 \dots

Apply long division:

\frac{- x ^{3} - 1.96995 \dots x ^{2} - 3.88073 \dots x - 9.64487 \dots}{x + 2.19936 \dots} = - x^{2} + 0.22941 \dots x - 4.38529 \dots

- x^{2} + 0.22941 \dots x - 4.38529 \dots \approx 0

Find one solution for

- x^{2} + 0.22941 \dots x - 4.38529 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.96995 \dots, x \approx - 2.19936 \dots

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

3 x^{4} - 48 x^{2} = 0

6 x^{4} - 54 x^{2} = 0

x^{3} + 2 = 0

y, (y - x)^{3} = c x

What are the solutions to the equation 2x-13=-x^4+6 ?
The solutions to the equation 2x-13=-x^4+6 are x\approx 1.96995…,x\approx-2.19936…
Find the zeros of 2x-13=-x^4+6
The zeros of 2x-13=-x^4+6 are x\approx 1.96995…,x\approx-2.19936…