What are the solutions to the equation -3x^{10}=5x-8 ?

The solutions to the equation -3x^{10}=5x-8 are x=1,x\approx-1.16507…

Find the zeros of -3x^{10}=5x-8

The zeros of -3x^{10}=5x-8 are x=1,x\approx-1.16507…

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- 3 x^{10} = 5 x - 8

x = 1, x \approx - 1.16507 \dots

Solution steps

- 3 x^{10} = 5 x - 8

Move

8

to the left side

- 3 x^{10} + 8 = 5 x

Move

5 x

to the left side

- 3 x^{10} + 8 - 5 x = 0

Write in the standard form

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

- 3 x^{10} - 5 x + 8 = 0

Factor

- 3 x^{10} - 5 x + 8 : - (x - 1) (3 x^{9} + 3 x^{8} + 3 x^{7} + 3 x^{6} + 3 x^{5} + 3 x^{4} + 3 x^{3} + 3 x^{2} + 3 x + 8)

- (x - 1) (3 x^{9} + 3 x^{8} + 3 x^{7} + 3 x^{6} + 3 x^{5} + 3 x^{4} + 3 x^{3} + 3 x^{2} + 3 x + 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or 3 x^{9} + 3 x^{8} + 3 x^{7} + 3 x^{6} + 3 x^{5} + 3 x^{4} + 3 x^{3} + 3 x^{2} + 3 x + 8 = 0

Solve

x - 1 = 0 : x = 1

Solve

3 x^{9} + 3 x^{8} + 3 x^{7} + 3 x^{6} + 3 x^{5} + 3 x^{4} + 3 x^{3} + 3 x^{2} + 3 x + 8 = 0 : x \approx - 1.16507 \dots

The solutions are

x = 1, x \approx - 1.16507 \dots

(2 n + 2) (n + 1) (n + 2) = 160

x^{4} - 12 x^{2} = - 32

1200 = 600 \cdot (1 + x)^{10}

r^{3} + 3 r^{2} - 4 = 0

x^{3} + \frac{5 x ^{2}}{2} + 4 x = 0

What are the solutions to the equation -3x^{10}=5x-8 ?
The solutions to the equation -3x^{10}=5x-8 are x=1,x\approx-1.16507…
Find the zeros of -3x^{10}=5x-8
The zeros of -3x^{10}=5x-8 are x=1,x\approx-1.16507…