Question 709876
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


{{{x = sqrt(-1)}}}


Our final two answers for x will be imaginary numbers.  Since {{{i = sqrt(-1)}}}, 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