Question

solve for f.
$f^2 + 10f + 25 = 0$
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
$f = \square$

Explanation:

Step1: Factor the quadratic equation

The quadratic equation \( f^2 + 10f + 25 = 0 \) can be factored as a perfect square trinomial. Recall that \( (a + b)^2 = a^2 + 2ab + b^2 \). Here, \( a = f \), \( 2ab = 10f \), so \( 2b = 10 \) which gives \( b = 5 \), and \( b^2 = 25 \). So the equation factors to \( (f + 5)^2 = 0 \).

Step2: Solve for f

Set \( f + 5 = 0 \) (since a square of a number is zero only when the number itself is zero). Solving for \( f \), we subtract 5 from both sides: \( f = -5 \).

Answer:

\( f = -5 \)