A) $$ 4 x+4=40 $$ B) $$ -2 x+1=-59 $$ C) $$ x: 2+2=200 $$ D) $$ x^{2}+9=900 $$

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**A) Resolver $$ 4x + 4 = 40 $$**

1. Restamos $$4$$ a ambos lados:
   $$
   4x + 4 - 4 = 40 - 4 \quad \Rightarrow \quad 4x = 36
   $$
2. Dividimos entre $$4$$ ambos lados:
   $$
   x = \frac{36}{4} = 9
   $$

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**B) Resolver $$ -2x + 1 = -59 $$**

1. Restamos $$1$$ a ambos lados:
   $$
   -2x + 1 - 1 = -59 - 1 \quad \Rightarrow \quad -2x = -60
   $$
2. Dividimos entre $$-2$$ ambos lados:
   $$
   x = \frac{-60}{-2} = 30
   $$

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**C) Resolver $$ \frac{x}{2} + 2 = 200 $$**

1. Restamos $$2$$ a ambos lados:
   $$
   \frac{x}{2} + 2 - 2 = 200 - 2 \quad \Rightarrow \quad \frac{x}{2} = 198
   $$
2. Multiplicamos ambos lados por $$2$$:
   $$
   x = 198 \times 2 = 396
   $$

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**D) Resolver $$ x^2 + 9 = 900 $$**

1. Restamos $$9$$ a ambos lados:
   $$
   x^2 + 9 - 9 = 900 - 9 \quad \Rightarrow \quad x^2 = 891
   $$
2. Extraemos la raíz cuadrada (recordando considerar ambas soluciones):
   $$
   x = \pm\sqrt{891}
   $$
3. Simplificamos la raíz:
   $$
   891 = 9 \times 99 = 9 \times 9 \times 11 = 81 \times 11 \quad \Rightarrow \quad \sqrt{891} = \sqrt{81 \times 11} = 9\sqrt{11}
   $$
   Por lo tanto,
   $$
   x = \pm 9\sqrt{11}
   $$
A) $$ x = 9 $$ B) $$ x = 30 $$ C) $$ x = 396 $$ D) $$ x = \pm 9\sqrt{11} $$

A)
B)
C)
D)

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