What are the solutions for the equation x^6+6x^3+5=0? Use factoring to solve

Step-by-step explanation:

Don't be fooled by this. We can make this look like the equations you have been factoring up to now. Let

x^3 = y Square both sides of the equation

(x^3) ^2 = y^2

x^6 = y^2

Now substitute these results into the given equation.

y^2 + 6y + 5 = 0

This factors

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

So either y + 5 = 0

or y + 1 = 0

y+5 = 0

x^3 + 5 = 0

x = cuberoot (-5)

x^3 + 1 = 0

x^3 = - 1

cube root (x^3) = cube root (-1)

x = - 1

Essentially the graph shows that there are only 2 roots (-1,0) (-1.71,0) just as our solution suggests.