What are the solutions to the equation 7x=6+5(3x+3)-x^6+5(3x+3)-x ?

The solutions to the equation 7x=6+5(3x+3)-x^6+5(3x+3)-x are x\approx-1.35501…,x\approx 2.08366…

Find the zeros of 7x=6+5(3x+3)-x^6+5(3x+3)-x

The zeros of 7x=6+5(3x+3)-x^6+5(3x+3)-x are x\approx-1.35501…,x\approx 2.08366…

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7 x = 6 + 5 (3 x + 3) - x^{6} + 5 (3 x + 3) - x

x \approx - 1.35501 \dots, x \approx 2.08366 \dots

Solution steps

7 x = 6 + 5 (3 x + 3) - x^{6} + 5 (3 x + 3) - x

Expand

6 + 5 (3 x + 3) - x^{6} + 5 (3 x + 3) - x : - x^{6} + 29 x + 36

7 x = - x^{6} + 29 x + 36

Switch sides

- x^{6} + 29 x + 36 = 7 x

Move

7 x

to the left side

- x^{6} + 22 x + 36 = 0

Find one solution for

- x^{6} + 22 x + 36 = 0

using Newton-Raphson:

x \approx - 1.35501 \dots

Apply long division:

\frac{- x ^{6} + 22 x + 36}{x + 1.35501 \dots} = - x^{5} + 1.35501 \dots x^{4} - 1.83606 \dots x^{3} + 2.48790 \dots x^{2} - 3.37114 \dots x + 26.56795 \dots

- x^{5} + 1.35501 \dots x^{4} - 1.83606 \dots x^{3} + 2.48790 \dots x^{2} - 3.37114 \dots x + 26.56795 \dots \approx 0

Find one solution for

- x^{5} + 1.35501 \dots x^{4} - 1.83606 \dots x^{3} + 2.48790 \dots x^{2} - 3.37114 \dots x + 26.56795 \dots = 0

using Newton-Raphson:

x \approx 2.08366 \dots

Apply long division:

\frac{- x ^{5} + 1.35501 \dots x ^{4} - 1.83606 \dots x ^{3} + 2.48790 \dots x ^{2} - 3.37114 \dots x + 26.56795 \dots}{x - 2.08366 \dots} = - x^{4} - 0.72865 \dots x^{3} - 3.35433 \dots x^{2} - 4.50140 \dots x - 12.75058 \dots

- x^{4} - 0.72865 \dots x^{3} - 3.35433 \dots x^{2} - 4.50140 \dots x - 12.75058 \dots \approx 0

Find one solution for

- x^{4} - 0.72865 \dots x^{3} - 3.35433 \dots x^{2} - 4.50140 \dots x - 12.75058 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 1.35501 \dots, x \approx 2.08366 \dots

x^{3} - 3 x - 52 = 0

6 x = x^{3}

5 x^{3} - 14 x^{2} - 3 x = 0

x^{2} (2 x + 1) = 0

x, x^{6} - 16 x^{4} = 0

What are the solutions to the equation 7x=6+5(3x+3)-x^6+5(3x+3)-x ?
The solutions to the equation 7x=6+5(3x+3)-x^6+5(3x+3)-x are x\approx-1.35501…,x\approx 2.08366…
Find the zeros of 7x=6+5(3x+3)-x^6+5(3x+3)-x
The zeros of 7x=6+5(3x+3)-x^6+5(3x+3)-x are x\approx-1.35501…,x\approx 2.08366…