I see you’ve uploaded a series of quadratic equations. Let’s go through the solutions for each problem step-by-step. Here are the general methods to solve these:

1. For equations of the form $x^2 = a$ (like #13 and #14), take the square root of both sides to solve for $x$.
2. For equations in standard form $ax^2 + bx + c = 0$ (like the others), use either factoring, completing the square, or the quadratic formula:
   $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Let’s solve a few to illustrate:

13. $x^2 = 64$

• Solution: $x = \pm \sqrt{64} = \pm 8$
• Answers: $x = 8$ or $x = -8$

14. $x^2 - 100 = 0$

• Rewrite as $x^2 = 100$
• Solution: $x = \pm \sqrt{100} = \pm 10$
• Answers: $x = 10$ or $x = -10$

15. $x^2 - 3x + 2 = 0$

• Factor as $(x - 1)(x - 2) = 0$
• Solutions: $x = 1$ and $x = 2$

16. $x^2 - 4x + 3 = 0$

• Factor as $(x - 1)(x - 3) = 0$
• Solutions: $x = 1$ and $x = 3$

If you'd like, I can continue solving each of these step-by-step or answer any specific ones you're struggling with.

Would you like to see detailed solutions for more, or do you have specific questions about these equations?

Here are five questions related to this topic for further exploration:

1. How does factoring differ from using the quadratic formula in solving quadratic equations?
2. Can every quadratic equation be solved by factoring? Why or why not?
3. What is the discriminant, and how does it determine the number and type of solutions in a quadratic equation?
4. How would you complete the square for equations like $x^2 - 3x + 2 = 0$?
5. What real-life scenarios can be modeled by quadratic equations?

Tip: Always check if a quadratic equation can be factored easily before using the quadratic formula; it can save time.