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

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

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

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

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x^{5} - 5 x = - 4

x = 1, x \approx - 1.65062 \dots

Solution steps

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^{3} - 3 x^{2} - 9 x + 26 = 0

5 x^{4} - 125 x^{2} = 0

3 x^{4} - 12 x^{2} + 12 = 0

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

x^{5} + 3 = x + 3

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