consider the following quadratic equation. x^2+2x+1=0 solve the quadratic equation by factoring.write your answer in reduced fraction form if necessary
To solve the quadratic equation by factoring, we need to factor the quadratic expression x^2 + 2x + 1 and then set each factor equal to zero to find the values of x.
Looking at the expression, we can see that it can be factored as (x + 1)(x + 1) or (x + 1)^2.
Setting (x + 1)^2 = 0, we get:
(x + 1) = 0
Now, solving for x, we subtract 1 from both sides:
x = -1
Therefore, the solution to the quadratic equation x^2 + 2x + 1 = 0 is x = -1, or in reduced fraction form, -1/1.