solve `x^(2)+4^(2)=9`

Answer

To solve the equation \( x^2 + 4^2 = 9 \), we can follow these steps:

### Step 1: Rewrite the equation
Start with the given equation:
\[ x^2 + 4^2 = 9 \]

### Step 2: Calculate \( 4^2 \)
Calculate \( 4^2 \):
\[ 4^2 = 16 \]
Now substitute this back into the equation:
\[ x^2 + 16 = 9 \]

### Step 3: Isolate \( x^2 \)
Next, isolate \( x^2 \) by subtracting 16 from both sides:
\[ x^2 = 9 - 16 \]

### Step 4: Simplify the right side
Calculate the right side:
\[ x^2 = -7 \]

### Step 5: Solve for \( x \)
Since \( x^2 = -7 \), we take the square root of both sides:
\[ x = \pm \sqrt{-7} \]

### Step 6: Express in terms of imaginary numbers
We can express \( \sqrt{-7} \) in terms of imaginary numbers:
\[ x = \pm \sqrt{7}i \]

### Final Answer
Thus, the solutions to the equation are:
\[ x = \sqrt{7}i \quad \text{and} \quad x = -\sqrt{7}i \]

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