Solve the equation: $$ \sqrt{x + 4} = 6 $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\sqrt{x + 4} = 6
$$

follow these steps:

### Step 1: Understand the Equation
The equation states that the square root of $$ x + 4 $$ is equal to 6.

### Step 2: Remove the Square Root
To eliminate the square root, square both sides of the equation:

$$
\left( \sqrt{x + 4} \right)^2 = 6^2
$$

This simplifies to:

$$
x + 4 = 36
$$

### Step 3: Solve for $$ x $$
Subtract 4 from both sides to isolate $$ x $$:

$$
x = 36 - 4
$$
$$
x = 32
$$

### Step 4: Check the Solution
It's good practice to substitute the solution back into the original equation to ensure it's correct.

$$
\sqrt{32 + 4} = \sqrt{36} = 6
$$

Since both sides of the equation are equal, $$ x = 32 $$ is the correct solution.

### **Answer:** 
$$ x = 32 $$
$$ x = 32 $$

Solve the equation: