What are the solutions to the equation 3x^2-x+54=3x^8+12 ?

The solutions to the equation 3x^2-x+54=3x^8+12 are x\approx 1.40878…,x\approx-1.41953…

Find the zeros of 3x^2-x+54=3x^8+12

The zeros of 3x^2-x+54=3x^8+12 are x\approx 1.40878…,x\approx-1.41953…

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3 x^{2} - x + 54 = 3 x^{8} + 12

x \approx 1.40878 \dots, x \approx - 1.41953 \dots

Solution steps

3 x^{2} - x + 54 = 3 x^{8} + 12

Switch sides

3 x^{8} + 12 = 3 x^{2} - x + 54

Move

54

to the left side

3 x^{8} - 42 = 3 x^{2} - x

Move

x

to the left side

3 x^{8} - 42 + x = 3 x^{2}

Move

3 x^{2}

to the left side

3 x^{8} - 42 + x - 3 x^{2} = 0

Write in the standard form

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

3 x^{8} - 3 x^{2} + x - 42 = 0

Find one solution for

3 x^{8} - 3 x^{2} + x - 42 = 0

using Newton-Raphson:

x \approx 1.40878 \dots

Apply long division:

\frac{3 x ^{8} - 3 x ^{2} + x - 42}{x - 1.40878 \dots} = 3 x^{7} + 4.22635 \dots x^{6} + 5.95401 \dots x^{5} + 8.38791 \dots x^{4} + 11.81675 \dots x^{3} + 16.64724 \dots x^{2} + 20.45236 \dots x + 29.81295 \dots

3 x^{7} + 4.22635 \dots x^{6} + 5.95401 \dots x^{5} + 8.38791 \dots x^{4} + 11.81675 \dots x^{3} + 16.64724 \dots x^{2} + 20.45236 \dots x + 29.81295 \dots \approx 0

Find one solution for

3 x^{7} + 4.22635 \dots x^{6} + 5.95401 \dots x^{5} + 8.38791 \dots x^{4} + 11.81675 \dots x^{3} + 16.64724 \dots x^{2} + 20.45236 \dots x + 29.81295 \dots = 0

using Newton-Raphson:

x \approx - 1.41953 \dots

Apply long division:

\frac{3 x ^{7} + 4.22635 \dots x ^{6} + 5.95401 \dots x ^{5} + 8.38791 \dots x ^{4} + 11.81675 \dots x ^{3} + 16.64724 \dots x ^{2} + 20.45236 \dots x + 29.81295 \dots}{x + 1.41953 \dots} = 3 x^{6} - 0.03226 \dots x^{5} + 5.99980 \dots x^{4} - 0.12904 \dots x^{3} + 11.99993 \dots x^{2} - 0.38710 \dots x + 21.00188 \dots

3 x^{6} - 0.03226 \dots x^{5} + 5.99980 \dots x^{4} - 0.12904 \dots x^{3} + 11.99993 \dots x^{2} - 0.38710 \dots x + 21.00188 \dots \approx 0

Find one solution for

3 x^{6} - 0.03226 \dots x^{5} + 5.99980 \dots x^{4} - 0.12904 \dots x^{3} + 11.99993 \dots x^{2} - 0.38710 \dots x + 21.00188 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.40878 \dots, x \approx - 1.41953 \dots

n^{3} - 6 n^{2} - 2 = 0

a^{3} + 5 a^{2} - 9 a - 45 = 0

x^{5} = - 125 x^{2}

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

x^{4} + 41 x^{2} + 400 = 0

What are the solutions to the equation 3x^2-x+54=3x^8+12 ?
The solutions to the equation 3x^2-x+54=3x^8+12 are x\approx 1.40878…,x\approx-1.41953…
Find the zeros of 3x^2-x+54=3x^8+12
The zeros of 3x^2-x+54=3x^8+12 are x\approx 1.40878…,x\approx-1.41953…