Factor the problem: $$ x^{2}-12 x+36 $$

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To factor the quadratic expression $$ x^{2} - 12x + 36 $$, follow these steps:

1. **Identify the coefficients:**
   - The quadratic is in the form $$ ax^2 + bx + c $$, where:
     - $$ a = 1 $$
     - $$ b = -12 $$
     - $$ c = 36 $$

2. **Find two numbers that multiply to $$ ac $$ and add to $$ b $$:**
   - Here, $$ ac = 1 \times 36 = 36 $$ and $$ b = -12 $$.
   - The two numbers that satisfy these conditions are **-6** and **-6**, since:
     - $$ -6 \times -6 = 36 $$
     - $$ -6 + -6 = -12 $$

3. **Express the quadratic in its factored form:**
   - Using the numbers found, the quadratic can be written as:
     $$
     (x - 6)(x - 6)
     $$
   - This can also be expressed as:
     $$
     (x - 6)^2
     $$

**Final Factored Form:**
$$
x^{2} - 12x + 36 = (x - 6)^2
$$
$$ x^{2} - 12x + 36 = (x - 6)^2 $$

Factor the problem: \( x^{2}-12 x+36 \)

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