Solve for all values of xx by factoring.
x, squared, plus, 6, x, plus, 10, equals, minus, x
x
2
+6x+10=
−x
To solve this equation by factoring, first move all terms to one side of the equation:
x^2 + 6x + 10 = -x
By adding x to both sides, we get:
x^2 + 7x + 10 = 0
Now, we need to factor the quadratic equation. The factors of the form x^2 + 7x + 10 can be written as (x + 2)(x + 5). Setting this equal to 0, we get:
(x + 2)(x + 5) = 0
By setting each factor equal to zero, we get the solutions for x:
x + 2 = 0
x = -2
x + 5 = 0
x = -5
Therefore, the solutions for x are x=-2 and x=-5.