Answer:
To factor the equation x^2 + 6x + 13, we can use the quadratic formula or factoring by grouping.
Using the quadratic formula, we can find the roots of the equation:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 6, and c = 13. Plugging these values into the formula, we get:
x = (-6 ± √(6^2 - 4(1)(13))) / 2(1)
x = (-6 ± √(36 - 52)) / 2
x = (-6 ± √(-16)) / 2
Since we have a negative value inside the square root, we know that the equation has no real roots. Therefore, it cannot be factored further using real numbers.
If you are looking to factor the equation using complex numbers, you can rewrite it as:
(x + 3 - 2i)(x + 3 + 2i)
These are the complex conjugate factors, and they give us the complete factorization of the equation.
Explanation: