Solve the equation:

[tex]\[
(x+7)(x-3) = (x+1)^2
\][/tex]

Select the correct choice below and fill in any answer boxes in your choice:

A. The solution set is [tex]\(\{\square\}\)[/tex]. (Simplify your answer.)
B. There is no solution.



Answer :

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].