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

The solutions to the equation 2-x=x^4 are x=1,x\approx-1.35320…

Find the zeros of 2-x=x^4

The zeros of 2-x=x^4 are x=1,x\approx-1.35320…

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2 - x = x^{4}

x = 1, x \approx - 1.35320 \dots

Solution steps

2 - x = x^{4}

Switch sides

x^{4} = 2 - x

Move

x

to the left side

x^{4} + x = 2

Move

2

to the left side

x^{4} + x - 2 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{3} + x^{2} + x + 2 = 0 : x \approx - 1.35320 \dots

The solutions are

x = 1, x \approx - 1.35320 \dots

4 x^{4} + x^{3} + x^{2} + x + 1 = 0

2 x^{3} + 3 x^{2} - 32 x + 15 = 0

3 x^{3} - 2 x^{2} - 82 x - 10 = 0

2 x^{4} - 12 x^{2} - 54 = 0

2 x^{3} - 24 x = 0

What are the solutions to the equation 2-x=x^4 ?
The solutions to the equation 2-x=x^4 are x=1,x\approx-1.35320…
Find the zeros of 2-x=x^4
The zeros of 2-x=x^4 are x=1,x\approx-1.35320…