Solve ` 16x^(2)+4=0`

Answer

To solve the equation \( 16x^2 + 4 = 0 \), we will follow these steps:

### Step 1: Rearrange the equation
First, we want to isolate the term with \( x^2 \). We do this by moving the constant term to the other side of the equation.

\[ 16x^2 = -4 \]

### Step 2: Divide by 16
Next, we divide both sides of the equation by 16 to solve for \( x^2 \).

\[ x^2 = \frac{-4}{16} \]

This simplifies to:

\[ x^2 = -\frac{1}{4} \]

### Step 3: Take the square root
Now, we take the square root of both sides. Remember that taking the square root of a negative number involves the imaginary unit \( i \), where \( i = \sqrt{-1} \).

\[ x = \pm \sqrt{-\frac{1}{4}} \]

### Step 4: Simplify the square root
We can separate the square root into its components:

\[ x = \pm \frac{\sqrt{-1}}{\sqrt{4}} \]

This simplifies to:

\[ x = \pm \frac{i}{2} \]

### Final Answer
Thus, the solutions to the equation \( 16x^2 + 4 = 0 \) are:

\[ x = \frac{i}{2} \quad \text{and} \quad x = -\frac{i}{2} \]

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