What are the solutions to the equation -4=x^5-5x ?

The solutions to the equation -4=x^5-5x are x=1,x\approx-1.65062…

Find the zeros of -4=x^5-5x

The zeros of -4=x^5-5x are x=1,x\approx-1.65062…

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- 4 = x^{5} - 5 x

x = 1, x \approx - 1.65062 \dots

Solution steps

- 4 = x^{5} - 5 x

Switch sides

x^{5} - 5 x = - 4

Move

4

to the left side

x^{5} - 5 x + 4 = 0

Factor

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

(x - 1)^{2} (x^{3} + 2 x^{2} + 3 x + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{3} + 2 x^{2} + 3 x + 4 = 0 : x \approx - 1.65062 \dots

The solutions are

x = 1, x \approx - 1.65062 \dots

x, x^{3} + y^{3} = 2

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

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

x^{3} - 5 x + 1 = - 0.8

x^{3} - 5 x^{2} + 4 x - 20 = 0

What are the solutions to the equation -4=x^5-5x ?
The solutions to the equation -4=x^5-5x are x=1,x\approx-1.65062…
Find the zeros of -4=x^5-5x
The zeros of -4=x^5-5x are x=1,x\approx-1.65062…