Let's solve the equation step-by-step:
Given:
[tex]\[
(x + 7)(x - 3) = (x + 1)^2
\][/tex]
First, we expand both sides of the equation.
Expanding the left-hand side:
[tex]\[
(x + 7)(x - 3) = x^2 - 3x + 7x - 21 = x^2 + 4x - 21
\][/tex]
Expanding the right-hand side:
[tex]\[
(x + 1)^2 = x^2 + 2x + 1
\][/tex]
Now, we can rewrite the equation with the expanded forms:
[tex]\[
x^2 + 4x - 21 = x^2 + 2x + 1
\][/tex]
Next, we subtract [tex]\(x^2 + 2x + 1\)[/tex] from both sides to simplify:
[tex]\[
x^2 + 4x - 21 - (x^2 + 2x + 1) = 0
\][/tex]
Simplify the equation:
[tex]\[
x^2 + 4x - 21 - x^2 - 2x - 1 = 0
\][/tex]
[tex]\[
2x - 22 = 0
\][/tex]
To isolate [tex]\(x\)[/tex], we add 22 to both sides:
[tex]\[
2x = 22
\][/tex]
Then, divide by 2:
[tex]\[
x = 11
\][/tex]
So, the solution set is:
[tex]\[
\{11\}
\][/tex]
The correct choice is:
A. The solution set is [tex]\(\{11\}\)[/tex].
