Now enter those coefficients into the quadratic formula below: $$ x=\frac{-2 \square \pm \sqrt{(\boxed{-2})^{2}-4 \cdot \sqrt[1]{11}}}{2 \cdot 1} $$ Now simplify the formula: $$ x=\frac{\square \pm \sqrt{\square}}{\square} $$

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Alright, I need to simplify the given quadratic formula step by step. The original formula is:

$$
x = \frac{-2 \square \pm \sqrt{(\boxed{-2})^{2} - 4 \cdot \sqrt[1]{11}}}{2 \cdot 1}
$$

First, let's identify the components of the formula. The quadratic formula is generally written as:

$$
x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}
$$

Comparing this with the given formula, it seems that $$ a = 1 $$, $$ b = -2 $$, and $$ c = \sqrt[1]{11} $$. However, the notation $$ \sqrt[1]{11} $$ is a bit unusual. Typically, the square root is denoted by $$ \sqrt{} $$, so I'll assume that $$ \sqrt[1]{11} $$ is a typo and should be $$ \sqrt{11} $$.

So, rewriting the formula with the corrected notation:

$$
x = \frac{-(-2) \pm \sqrt{(-2)^{2} - 4 \cdot \sqrt{11}}}{2 \cdot 1}
$$

Simplifying the numerator:

1. $$ -(-2) = 2 $$
2. $$ (-2)^{2} = 4 $$
3. $$ 4 \cdot \sqrt{11} = 4\sqrt{11} $$

So, the formula becomes:

$$
x = \frac{2 \pm \sqrt{4 - 4\sqrt{11}}}{2}
$$

Next, I'll simplify the expression under the square root:

$$
4 - 4\sqrt{11}
$$

This can be factored as:

$$
4(1 - \sqrt{11})
$$

So, the formula now is:

$$
x = \frac{2 \pm \sqrt{4(1 - \sqrt{11})}}{2}
$$

The square root of a product is the product of the square roots:

$$
\sqrt{4(1 - \sqrt{11})} = \sqrt{4} \cdot \sqrt{1 - \sqrt{11}} = 2\sqrt{1 - \sqrt{11}}
$$

Substituting back into the formula:

$$
x = \frac{2 \pm 2\sqrt{1 - \sqrt{11}}}{2}
$$

Now, I can factor out the 2 in the numerator:

$$
x = \frac{2(1 \pm \sqrt{1 - \sqrt{11}})}{2}
$$

The 2 in the numerator and the 2 in the denominator cancel each other out:

$$
x = 1 \pm \sqrt{1 - \sqrt{11}}
$$

So, the simplified form of the quadratic formula is:

$$
x = 1 \pm \sqrt{1 - \sqrt{11}}
$$

$$ x = 1 \pm \sqrt{1 - \sqrt{11}} $$

Now enter those coefficients into the quadratic formula below: \( x=\frac{-2 \square \pm \sqrt{(\boxed{-2})^{2}-4 \cdot \sqrt[1]{11}}}{2 \cdot 1} \) Now simplify the formula: \( x=\frac{\square \pm \sqrt{\square}}{\square} \)

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