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# What are the solutions of the equation x^{6} + 6x^{3} + 5 = 0? Use factoring to solve.

**Solution:**

Given, the equation is x^{6} + 6x^{3} + 5 = 0

We have to find the solution of the equation by factoring.

Let x^{3} = y

Equation becomes y^{2} + 6y + 5 = 0

y^{2} + 5y + y + 5 = 0

y(y + 5) + 1(y + 5) = 0

(y + 5)(y + 1) = 0

To find the solution,

y + 5 = 0

y = -5

y + 1 = 0

y = -1

When, y = -1,

x^{3} = (-1)^{3}

Taking cube root,

x = -1

When, y = -5,

x^{3} = (-5)^{3} =

x^{3} = -125

Taking cube root,

x = ∛-5

Therefore, the solutions are x = -1 and x = ∛-5

## What are the solutions of the equation x^{6} + 6x^{3} + 5 = 0? Use factoring to solve.

**Summary:**

The solutions to the equation x^{6} + 6x^{3} + 5 = 0 by factoring are x = -1 and x = ∛-5.

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