To solve the equation \( 8 - x^2 = 4 \), follow these steps:

1. Subtract 8 from both sides to isolate the \( x^2 \) term:
   \[
   8 - x^2 - 8 = 4 - 8
   \]
   Simplifying this:
   \[
   -x^2 = -4
   \]

2. Multiply both sides by \(-1\) to get rid of the negative sign:
   \[
   x^2 = 4
   \]

3. Take the square root of both sides:
   \[
   x = \pm \sqrt{4}
   \]
   \[
   x = \pm 2
   \]

So, the solutions are \( x = 2 \) and \( x = -2 \).

Would you like more details on any step or have any further questions?

Here are some related questions you might find useful:

1. How can I solve quadratic equations in general?
2. What are the steps for completing the square?
3. How do you graph \( x^2 \) equations?
4. Can quadratic equations have complex solutions?
5. How does the quadratic formula work?

**Tip:** Always remember to check both positive and negative roots when solving equations involving squares!

Learn how to solve the quadratic equation 8 - x^2 = 4 through a clear, step-by-step solution. This example demonstrates important algebraic techniques like isolating the square term and applying the square root principle. Ideal for students in Grades 8-10.

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