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1. Is [tex] x = -12 [/tex] a solution of [tex] x^2 + 10x + 25 = 49 [/tex]? Explain.

A. No, because [tex] (-12)^2 + 10(-12) + 25 \neq 49 [/tex].

B. Yes, because the graph of the equation will cross the y-axis at [tex] x = -12 [/tex].

C. No, because the graph of the equation does not touch the x-axis.

D. Yes, because [tex] (-12)^2 + 10(-12) + 25 = 49 [/tex].

Sagot :

GinnyAnswer
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]."
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