Solve by factoring.c squared plus 10 c plus 16 equals 0Question content area bottomPart 1The solution is c ​=enter your response here.​(Use a comma to separate answers as​ needed.)

Answer 1

To solve the quadratic equation \( c^2 + 10c + 16 = 0 \) by factoring, we need to look for two numbers that multiply to 16 (the constant term) and add to 10 (the coefficient of the linear term).

The factors of 16 that add up to 10 are 2 and 8.

Thus, we can factor the equation as follows:

\[ (c + 2)(c + 8) = 0 \]

Next, we set each factor to zero to find the solutions for \( c \):

1. \( c + 2 = 0 \) → \( c = -2 \)
2. \( c + 8 = 0 \) → \( c = -8 \)

Therefore, the solutions are:

\[ c = -2, -8 \]

So the final answer is:

c = -2, -8