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## Sagot :

### Step 1: Simplify the equation

First, we need to move all terms to one side of the equation to set it equal to zero.

[tex]\[ x^2 + 20x + 100 - 36 = 0 \][/tex]

Simplify the constants on the left-hand side:

[tex]\[ x^2 + 20x + 64 = 0 \][/tex]

### Step 2: Identify coefficients

The simplified equation is in the standard form of a quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex], where:

- [tex]\(a = 1\)[/tex]

- [tex]\(b = 20\)[/tex]

- [tex]\(c = 64\)[/tex]

### Step 3: Use the quadratic formula

The quadratic formula is given by:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

Substitute [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] into the formula:

[tex]\[ x = \frac{-20 \pm \sqrt{20^2 - 4 \cdot 1 \cdot 64}}{2 \cdot 1} \][/tex]

### Step 4: Calculate the discriminant

Calculate the value inside the square root (the discriminant):

[tex]\[ b^2 - 4ac = 20^2 - 4 \cdot 1 \cdot 64 \][/tex]

[tex]\[ = 400 - 256 \][/tex]

[tex]\[ = 144 \][/tex]

### Step 5: Solve for [tex]\(x\)[/tex]

Now plug the discriminant back into the quadratic formula:

[tex]\[ x = \frac{-20 \pm \sqrt{144}}{2 \cdot 1} \][/tex]

[tex]\[ x = \frac{-20 \pm 12}{2} \][/tex]

### Step 6: Compute the two possible solutions

Solve for the two values of [tex]\(x\)[/tex]:

[tex]\[ x_1 = \frac{-20 + 12}{2} = \frac{-8}{2} = -4 \][/tex]

[tex]\[ x_2 = \frac{-20 - 12}{2} = \frac{-32}{2} = -16 \][/tex]

Thus, the solutions to the equation are [tex]\(x = -4\)[/tex] and [tex]\(x = -16\)[/tex].

### Step 7: Identify the correct multiple-choice answer

From the given multiple-choice options:

- [tex]\(x = -16\)[/tex] or [tex]\(x = -4\)[/tex]

- [tex]\(x = -10\)[/tex]

- [tex]\(x = -8\)[/tex]

- [tex]\(x = 4\)[/tex] or [tex]\(x = 16\)[/tex]

The correct choice corresponds to the option where [tex]\(x = -16\)[/tex] or [tex]\(x = -4\)[/tex].

Therefore, the answer is:

[tex]\[ \boxed{1} \][/tex]