$$ 1 \leftarrow \quad $$ Solve the quadratic equation $$ 36=(x+4)^{2} $$

Question

UpStudy AI · Accepted Answer

To solve the quadratic equation:

$$
36 = (x + 4)^2
$$

**Step 1: Take the Square Root of Both Sides**

$$
\sqrt{36} = \sqrt{(x + 4)^2}
$$

$$
6 = |x + 4|
$$

This implies two possible equations:

$$
x + 4 = 6 \quad \text{or} \quad x + 4 = -6
$$

**Step 2: Solve Each Equation Separately**

1. **First Equation:**
   $$
   x + 4 = 6
   $$
   Subtract 4 from both sides:
   $$
   x = 6 - 4
   $$
   $$
   x = 2
   $$

2. **Second Equation:**
   $$
   x + 4 = -6
   $$
   Subtract 4 from both sides:
   $$
   x = -6 - 4
   $$
   $$
   x = -10
   $$

**Solution:**

The quadratic equation $$ 36 = (x + 4)^2 $$ has two solutions:

$$
x = 2 \quad \text{and} \quad x = -10
$$
The solutions are $$ x = 2 $$ and $$ x = -10 $$.

\( 1 \leftarrow \quad \) Solve the quadratic equation \( 36=(x+4)^{2} \)