Solve the equation using inverse operations. Check your solutions. In you final answer, include all of your work.

Question

-x^2 = -36

Answer 1

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 2

can you do it without all the symbols and slashes

Answer 3

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 4

can you use less words and make it less advamced

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.