Question

Use the rules of equations and inverse operations to solve the equation. In your final answer, include all of your work.
4-x^2=-16

Answer 1

To solve the equation \( 4 - x^2 = -16 \), we will follow the steps using algebraic operations.

### Step 1: Isolate the term with \( x^2 \)
Start by moving 4 to the right side of the equation.

\[
4 - x^2 = -16
\]

Subtracting 4 from both sides:

\[
-x^2 = -16 - 4
\]

This simplifies to:

\[
-x^2 = -20
\]

### Step 2: Multiply both sides by -1
To eliminate the negative sign in front of \( x^2 \), multiply both sides of the equation by -1:

\[
x^2 = 20
\]

### Step 3: Solve for \( x \) by taking the square root
To solve for \( x \), take the square root of both sides. Remember, taking the square root of a number gives both a positive and negative solution.

\[
x = \pm \sqrt{20}
\]

### Step 4: Simplify \( \sqrt{20} \)
Now, simplify \( \sqrt{20} \):

\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
\]

### Step 5: Write the final solutions
Now, incorporate the positive and negative solutions:

\[
x = \pm 2\sqrt{5}
\]

Thus, the final answer is:

\[
x = 2\sqrt{5} \quad \text{or} \quad x = -2\sqrt{5}
\]

These are the solutions to the equation \( 4 - x^2 = -16 \).