To solve the equation \(-x^2 = -36\) using inverse operations, follow these steps:
Step 1: Isolate \(x^2\)
First, we can eliminate the negative sign on both sides of the equation. Multiply both sides by \(-1\):
\[ x^2 = 36 \]
Step 2: Take the square root of both sides
Next, we take the square root of both sides to solve for \(x\). Remember that taking the square root introduces both the positive and negative solutions:
\[ x = \pm \sqrt{36} \]
Since \(\sqrt{36} = 6\), we have:
\[ x = 6 \quad \text{or} \quad x = -6 \]
Step 3: Write the final solutions
Thus, the solutions to the equation are:
\[ x = 6 \quad \text{and} \quad x = -6 \]
Step 4: Check the solutions
Now, we will check both solutions by substituting them back into the original equation.
Check \(x = 6\):
\[ -x^2 = -36 \] Substituting \(x = 6\):
\[ -(6)^2 = -36 \ -36 = -36 \quad \text{(True)} \]
Check \(x = -6\):
Now substitute \(x = -6\):
\[ -(-6)^2 = -36 \ -36 = -36 \quad \text{(True)} \]
Conclusion
Both values satisfy the original equation. Therefore, the final solutions are:
\[ \boxed{6 \text{ and } -6} \]