To determine if [tex]\(x = -12\)[/tex] is a solution to the equation [tex]\(x^2 + 10x + 25 = 49\)[/tex], let's substitute [tex]\(x = -12\)[/tex] into the equation and determine if both sides are equal.
1. Substitute [tex]\(x = -12\)[/tex] into the left-hand side of the equation:
[tex]\[
(-12)^2 + 10(-12) + 25
\][/tex]
2. Calculate each term:
[tex]\[
(-12)^2 = 144
\][/tex]
[tex]\[
10(-12) = -120
\][/tex]
[tex]\[
25 = 25
\][/tex]
3. Add these results together:
[tex]\[
144 - 120 + 25 = 49
\][/tex]
4. Compare the left-hand side with the right-hand side of the original equation:
[tex]\[
49 = 49
\][/tex]
Since both sides of the equation are equal when [tex]\(x = -12\)[/tex], we can conclude that [tex]\(x = -12\)[/tex] is indeed a solution to the equation [tex]\(x^2 + 10x + 25 = 49\)[/tex].
Thus, the correct answer is:
"Yes, because [tex]\((-12)^2 + 10(-12) + 25 = 49\)[/tex]."
