Solved Examples: Quadratic Equations Using the Square Root Property

📚 Quick Study Guide

• 🔢 The Square Root Property: If $x^2 = a$, then $x = \pm \sqrt{a}$.
• ➕ When $a > 0$, there are two real solutions.
• ➖ When $a < 0$, there are two imaginary solutions.
• 0️⃣ When $a = 0$, there is one real solution (x=0).
• 💡Isolate the squared term before applying the square root property.
• ✏️ Remember to consider both positive and negative roots.

Practice Quiz

1. What are the solutions to the equation $x^2 = 25$?
   1. 5
   2. -5
   3. 5 and -5
   4. No real solutions
2. Solve for $x$: $(x - 3)^2 = 16$
   1. 7
   2. -1
   3. 7 and -1
   4. No real solutions
3. Find the solutions to $x^2 + 9 = 0$
   1. 3
   2. -3
   3. 3 and -3
   4. No real solutions
4. Solve for $x$: $4x^2 = 36$
   1. 3
   2. -3
   3. 3 and -3
   4. 9 and -9
5. What are the solutions to $(2x + 1)^2 = 9$?
   1. 1
   2. -2
   3. 1 and -2
   4. 2 and -4
6. Find the solution(s) to the equation $x^2 - 64 = 0$
   1. 8
   2. -8
   3. 8 and -8
   4. No real solutions
7. Solve for $x$: $3x^2 - 27 = 0$
   1. 3
   2. -3
   3. 3 and -3
   4. 9 and -9