Answer:
To solve this equation, we need to factor the quadratic expression on the left side.
x² + x = 0
We can factor the quadratic by finding two numbers that multiply to give x² and add to give x. In this case, we can see that the numbers -1 and 1 multiply to give -1, and add to give 0.
x² + x = 0
(x + 1)(x - 1) = 0
Next, we can set each factor equal to 0 and solve for x.
x + 1 = 0
x = -1
x - 1 = 0
x = 1
Therefore, the solutions to the equation x² + x = 0 are x = -1 and x = 1. These are the only values of x that make the equation true.