What are the solutions to the equation 4x^3+x^7=-5 ?

The solutions to the equation 4x^3+x^7=-5 are x=-1

Find the zeros of 4x^3+x^7=-5

The zeros of 4x^3+x^7=-5 are x=-1

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4 x^{3} + x^{7} = - 5

x = - 1

Solution steps

4 x^{3} + x^{7} = - 5

Move

5

to the left side

4 x^{3} + x^{7} + 5 = 0

Write in the standard form

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

x^{7} + 4 x^{3} + 5 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

x^{6} - x^{5} + x^{4} - x^{3} + 5 x^{2} - 5 x + 5 = 0 :

No Solution for

x \in R

The solution is

x = - 1

\frac{7}{18} = 21 x^{6}

x^{3} + 0.1 x^{2} + 0.4 x = 1.2

5 x^{3} - 9 x^{2} + 28 x + 6 = 0

x^{3} + 2 x^{2} - 3 x - 6

y, 8 y^{3} - 1 = 0

What are the solutions to the equation 4x^3+x^7=-5 ?
The solutions to the equation 4x^3+x^7=-5 are x=-1
Find the zeros of 4x^3+x^7=-5
The zeros of 4x^3+x^7=-5 are x=-1