SOLUTION: Solve the following: x^3 + 2x^2 = -5x

Question 113859: Solve the following: x^3 + 2x^2 = -5x
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Move all of the terms to the left side

Factor out the GCF

or Set each factor equal to zero

So this means we have one solution of x=0

Now let's focus on the second equation

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=2, and c=5

Square 2 to get 4

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

After simplifying, the quadratic has roots of

or

Notice if we graph the quadratic , we get

graph of

And we can see that there are no real roots

To visually verify the answer, check out this page to see a visual representation of imaginary roots

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Answer:

So we have the solutions : , or

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