Question 709876: How do you solve x^3+x=0 ?
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! To solve for x, first factor an x from the left side of the equal sign, since x is common to both terms. This gives us
x(x^2 + 1) = 0
We know that x = 0, because if you multiply any number by 0, you get zero, so if you substitute 0 into the factored equation
0(0^2 + 1)
We get 0.
Now, to find the other values of x, set (x^2 + 1) equal to 0: x^2 + 1 = 0
To solve for x, subtract 1 from both sides of the equation, which gives us
x^2 = -1
Since we are squaring the x, we must take the square root of both sides, to remove the exponent of 2. This gives us
Our final two answers for x will be imaginary numbers. Since  , i will be the second value of x. Remember, when you take the square root of a square, your result is both a positive AND negative number. Therefore, your third and final value of x, is -i
Answer: x = 0, i, -i
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