Alright, let's solve the given equation step-by-step:
The equation given is [tex]\((x - 3)^2 = 49\)[/tex].
First, we need to eliminate the square by taking the square root on both sides of the equation:
[tex]\[
\sqrt{(x - 3)^2} = \sqrt{49}
\][/tex]
This results in:
[tex]\[
|x - 3| = 7
\][/tex]
The absolute value equation [tex]\(|x - 3| = 7\)[/tex] implies two possible scenarios:
1. [tex]\(x - 3 = 7\)[/tex]
2. [tex]\(x - 3 = -7\)[/tex]
Let's solve for [tex]\(x\)[/tex] in each case:
1. [tex]\(x - 3 = 7\)[/tex]
[tex]\[
x = 7 + 3
\][/tex]
[tex]\[
x = 10
\][/tex]
2. [tex]\(x - 3 = -7\)[/tex]
[tex]\[
x = -7 + 3
\][/tex]
[tex]\[
x = -4
\][/tex]
Thus, the solutions to the equation [tex]\((x - 3)^2 = 49\)[/tex] are:
[tex]\[
x = 10 \quad \text{and} \quad x = -4
\][/tex]
So, checking each option:
A. [tex]\(x = -7\)[/tex] is not a solution.
B. [tex]\(x = 10\)[/tex] is a solution.
C. [tex]\(x = 7\)[/tex] is not a solution.
D. [tex]\(x = -4\)[/tex] is a solution.
E. [tex]\(x = -10\)[/tex] is not a solution.
Therefore, the correct options are:
B. [tex]\(x = 10\)[/tex]
D. [tex]\(x = -4\)[/tex]
