Test questions on solving x squared equals k equations

📚 Quick Study Guide

• 🔢 Isolate $x^2$ on one side of the equation: Make sure your equation is in the form $x^2 = k$.
• ➕ Take the square root of both sides: Remember to consider both the positive and negative square roots. So, $x = \pm \sqrt{k}$.
• 🤔 Simplify the square root: If possible, simplify the square root. For example, $\sqrt{9} = 3$.
• ✅ Write out both solutions: You'll have two solutions: $x = \sqrt{k}$ and $x = -\sqrt{k}$.
• 💡 If $k < 0$: There are no real solutions to the equation $x^2 = k$.

📝 Practice Quiz

1. What are the solutions to the equation $x^2 = 25$?
   1. x = 5
   2. x = -5
   3. x = 5, x = -5
   4. No real solutions
2. Solve for x: $x^2 = 49$
   1. x = 7
   2. x = -7
   3. x = 7, x = -7
   4. x = 14
3. What are the real solutions of $x^2 = -16$?
   1. x = 4
   2. x = -4
   3. x = 4, x = -4
   4. No real solutions
4. Find the solutions to $x^2 = 144$.
   1. x = 12
   2. x = -12
   3. x = 12, x = -12
   4. x = 72
5. What is the solution set for $x^2 - 9 = 0$?
   1. {3}
   2. {-3}
   3. {3, -3}
   4. {9}
6. Solve: $2x^2 = 50$
   1. x = 5
   2. x = -5
   3. x = 5, x = -5
   4. x = 25
7. What are the solutions to $(x+1)^2 = 9$?
   1. x = 2
   2. x = -4
   3. x = 2, x = -4
   4. No real solutions