What are the solutions to the equation 2x^4-x^3-2x+23x=-2 ?

The solutions to the equation 2x^4-x^3-2x+23x=-2 are x=-2,x\approx-0.09528…

Find the zeros of 2x^4-x^3-2x+23x=-2

The zeros of 2x^4-x^3-2x+23x=-2 are x=-2,x\approx-0.09528…

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2 x^{4} - x^{3} - 2 x + 23 x = - 2

x = - 2, x \approx - 0.09528 \dots

Solution steps

2 x^{4} - x^{3} - 2 x + 23 x = - 2

Refine

2 x^{4} - x^{3} + 21 x = - 2

Move

2

to the left side

2 x^{4} - x^{3} + 21 x + 2 = 0

Factor

2 x^{4} - x^{3} + 21 x + 2 : (x + 2) (2 x^{3} - 5 x^{2} + 10 x + 1)

(x + 2) (2 x^{3} - 5 x^{2} + 10 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 2 = 0 or 2 x^{3} - 5 x^{2} + 10 x + 1 = 0

Solve

x + 2 = 0 : x = - 2

Solve

2 x^{3} - 5 x^{2} + 10 x + 1 = 0 : x \approx - 0.09528 \dots

The solutions are

x = - 2, x \approx - 0.09528 \dots

4 x^{3} - 2 = 2 x + 33 - 1

y - y^{9} = 0

x^{4} - 48 x^{2} + 512 = 0

(2 x - 3) (x^{2} - 16) = 0

3 x^{3} + 2 x^{2} - 7 x + 2 = 0

What are the solutions to the equation 2x^4-x^3-2x+23x=-2 ?
The solutions to the equation 2x^4-x^3-2x+23x=-2 are x=-2,x\approx-0.09528…
Find the zeros of 2x^4-x^3-2x+23x=-2
The zeros of 2x^4-x^3-2x+23x=-2 are x=-2,x\approx-0.09528…