rewrite the equation by solving for x.  y=x^(2) -100

To solve for \( x \) in the equation \( y = x^2 - 100 \), follow these steps:

1. Start with the given equation:
   \[
   y = x^2 - 100
   \]

2. Add 100 to both sides to isolate the \( x^2 \) term:
   \[
   y + 100 = x^2
   \]

3. Take the square root of both sides:
   \[
   x = \pm \sqrt{y + 100}
   \]

So, the solution for \( x \) is:
\[
x = \pm \sqrt{y + 100}
\]

Would you like more details on any step? 

Here are five related questions to explore further:

1. What happens if \( y \) is negative in the equation \( x = \pm \sqrt{y + 100} \)?
2. How would the equation change if it were \( y = x^2 + 100 \)?
3. What are the restrictions on \( y \) for this equation to have real solutions?
4. How do you graph the equation \( y = x^2 - 100 \)?
5. How do you solve for \( y \) if \( x = 3 \)?

**Tip:** When solving for a variable that involves a square, always remember to consider both the positive and negative square roots.

rewrite the equation by solving for x. y=x^(2) -100

Explore how to solve for x in the quadratic equation y = x^2 - 100 with step-by-step instructions. This problem involves isolating the x variable using square roots. Learn the solution process, suitable for students in Grades 7-9.

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