To solve the equation \(56^2 + x^2 = 70^2\) for \(x\), follow these steps:

1. Start by squaring the numbers:
   \[
   56^2 = 3136
   \]
   \[
   70^2 = 4900
   \]

2. Substitute these values into the equation:
   \[
   3136 + x^2 = 4900
   \]

3. Subtract 3136 from both sides of the equation to isolate \(x^2\):
   \[
   x^2 = 4900 - 3136
   \]
   \[
   x^2 = 1764
   \]

4. Finally, take the square root of both sides to solve for \(x\):
   \[
   x = \sqrt{1764}
   \]
   \[
   x = 42
   \]

So, the solution is \(x = 42\).

Would you like more details or have any questions?

Here are 5 related questions:
1. Can you solve the equation \(x^2 + 144 = 900\) for \(x\)?
2. What happens if the squared term is negative?
3. How do you solve the equation \(x^2 + y^2 = z^2\) in general?
4. Can you solve \(x^2 + 9 = 0\) over the real numbers?
5. How do you determine the hypotenuse in a right triangle?

**Tip:** When solving equations involving squares, always remember to consider both the positive and negative roots if applicable.

Learn how to solve the equation 56^2 + x^2 = 70^2 step-by-step. This problem involves algebraic manipulation and application of the Pythagorean theorem. Suitable for high school students.

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