Interactive quiz: Solving perfect square quadratics by square roots

📚 Quick Study Guide

• 🔢 Definition: A perfect square quadratic is a quadratic equation that can be written in the form $(ax + b)^2 = c$ or $(ax - b)^2 = c$.
• ➗ Isolate the Squared Term: Get the squared term alone on one side of the equation.
• ✅ Take the Square Root: Take the square root of both sides of the equation, remembering to consider both the positive and negative roots.
• ➕ Solve for $x$: Solve the resulting two linear equations for $x$.
• ✍️ Formula: If $(x + a)^2 = b$, then $x + a = \pm \sqrt{b}$, and $x = -a \pm \sqrt{b}$.

🧪 Practice Quiz

1. Question 1: What are the solutions to the equation $(x + 3)^2 = 16$?
   1. A) $x = 1, -7$
   2. B) $x = -1, 7$
   3. C) $x = 1, 7$
   4. D) $x = -1, -7$
2. Question 2: Solve for $x$: $(x - 5)^2 = 9$
   1. A) $x = 2, 8$
   2. B) $x = -2, -8$
   3. C) $x = -2, 8$
   4. D) $x = 2, -8$
3. Question 3: What are the roots of $(2x + 1)^2 = 25$?
   1. A) $x = 2, -3$
   2. B) $x = -2, 3$
   3. C) $x = 2, 3$
   4. D) $x = -2, -3$
4. Question 4: Find the solution set for $(x + 4)^2 = 0$.
   1. A) ${4}$
   2. B) ${-4}$
   3. C) ${0, -4}$
   4. D) ${0, 4}$
5. Question 5: Solve: $(3x - 2)^2 = 49$
   1. A) $x = 3, -\frac{5}{3}$
   2. B) $x = -3, \frac{5}{3}$
   3. C) $x = 3, \frac{5}{3}$
   4. D) $x = -3, -\frac{5}{3}$
6. Question 6: What value(s) of $x$ satisfy $(x - 1)^2 - 36 = 0$?
   1. A) $x = 7, -5$
   2. B) $x = -7, 5$
   3. C) $x = 7, 5$
   4. D) $x = -7, -5$
7. Question 7: Determine the solution to $(4x + 3)^2 = 1$.
   1. A) $x = -\frac{1}{2}, -1$
   2. B) $x = \frac{1}{2}, 1$
   3. C) $x = \frac{1}{2}, -1$
   4. D) $x = -\frac{1}{2}, 1$