Final answer:
The quadratic expression x^2+13x+13 cannot be factorized into integers. To solve for x, we would use the quadratic formula and find that the solutions involve square roots, as they are not neat integers.
Step-by-step explanation:
To factorize the quadratic expression x^2+13x+13, we look for two numbers that multiply to the constant term (13) and add up to the coefficient of the linear term (13). Unfortunately, there are no two integers that satisfy both these conditions. So, this quadratic expression is prime and cannot be factorized over the integers.
If we still want to solve the equation x^2 + 13x + 13 = 0, we would need to use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = 13, and c = 13.
Applying the quadratic formula, we get:
- Calculate the discriminant: (13)^2 - 4(1)(13) = 169 - 52 = 117.
- Find the two solutions:
- x = (-13 + √117) / 2
- x = (-13 - √117) / 2
Thus, the solutions are not integers but involve square roots. This is a very common scenario in algebra where not all quadratics can be easily factorized.
o factorize the expression x^2+13x+13, we need to find two numbers that add up to 13 (coefficient of x) and multiply to 13 (constant term).
Since 13 is a prime number, the only possibilities are 1 and 13.
Therefore, the factored form of x^2+13x+13 is (x+1)(x+13).