Question

Solve the equation using inverse operations. Check your solutions. In you final answer, include all of your work.
-x^2 = -36

Answer 1

can you do it without all the symbols and slashes

Answer 2

can you use less words and make it less advamced

Answer 3

To solve the equation \(-x^2 = -36\), we will first isolate \(x^2\) and then solve for \(x\) using inverse operations.

### Step 1: Eliminate the negative sign
Multiply both sides of the equation by \(-1\):
\[
x^2 = 36
\]

### Step 2: Take the square root
To solve for \(x\), we take the square root of both sides. Remember to consider both the positive and negative square roots:
\[
x = \pm \sqrt{36}
\]

### Step 3: Calculate the square root
Since \(\sqrt{36} = 6\), we have:
\[
x = 6 \quad \text{or} \quad x = -6
\]

### Step 4: Verify the solutions
Now, we will check both potential solutions by substituting them back into the original equation.

#### Checking \(x = 6\):
\[
-x^2 = -36
\]
Substituting \(x = 6\):
\[
-(6)^2 = -36
\]
Calculating:
\[
-36 = -36 \quad \text{(True)}
\]

#### Checking \(x = -6\):
\[
-x^2 = -36
\]
Substituting \(x = -6\):
\[
-(-6)^2 = -36
\]
Calculating:
\[
-36 = -36 \quad \text{(True)}
\]

### Final answer
Both solutions satisfy the original equation. Therefore, the solutions are:
\[
\boxed{6 \text{ and } -6}
\]

Answer 4

Sure! Let’s solve the equation step by step without using symbols and slashes.

**Step 1: Start with the equation**

The equation is negative x squared equals negative thirty-six.

**Step 2: Eliminate the negative sign**

To eliminate the negative sign on both sides, we can multiply the entire equation by negative one. This changes the equation to:

x squared equals thirty-six.

**Step 3: Take the square root**

Now, we want to find what x is. To do this, we take the square root of both sides. Remember that both positive and negative roots need to be considered.

So we find:

x equals positive six or x equals negative six.

**Step 4: Check the solutions**

Now let us check our solutions by substituting them back into the original equation.

**Checking x equals six:**

Substituting six back into the original equation gives us:

Negative six squared equals negative thirty-six.

Calculating this gives us:

Negative thirty-six equals negative thirty-six, which is true.

**Checking x equals negative six:**

Now substituting negative six back gives us:

Negative negative six squared equals negative thirty-six.

Calculating this gives us:

Negative thirty-six equals negative thirty-six, which is also true.

**Final answer:**

Both solutions are correct, so the final answers are six and negative six.

Answer 5

Of course! Here’s a simpler version with fewer words:

**Start with the equation:**

Negative x squared equals negative thirty-six.

**Step 1: Get rid of negatives**

Multiply both sides by negative one:

x squared equals thirty-six.

**Step 2: Take the square root**

x equals six or x equals negative six.

**Step 3: Check the answers**

For x equals six:

Negative six squared equals negative thirty-six.

This works since negative thirty-six equals negative thirty-six.

For x equals negative six:

Negative negative six squared equals negative thirty-six.

This also works since negative thirty-six equals negative thirty-six.

**Final answer:**

The answers are six and negative six.