To complete the last step:
First, we write each trinomial as a binomial squared:
- The [tex]\(x\)[/tex]-terms: [tex]\(x^2 + 12x + 36\)[/tex]
[tex]\[
x^2 + 12x + 36 = (x + 6)^2
\][/tex]
- The [tex]\(y\)[/tex]-terms: [tex]\(y^2 + 2y + 1\)[/tex]
[tex]\[
y^2 + 2y + 1 = (y + 1)^2
\][/tex]
Next, we simplify the right side of the equation:
- Combining all constants on the right-hand side:
[tex]\[
1 + 36 + 1 = 38
\][/tex]
Therefore, the equation becomes:
[tex]\[
(x + 6)^2 + (y + 1)^2 = 38
\][/tex]
So, the final result in standard form is:
[tex]\[
(x + 6)^2 + (y + 1)^2 = 38
\][/tex]