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only answer number 1 3 5 7 9 (the green board is where the examples are located)

Let's solve the given quadratic equations based on the examples from the green board (Factoring and Completing the Square methods). We will use the appropriate method for each problem.

1. \( x^2 + 10x + 9 = 0 \)

   We can solve this by factoring. We need to find two numbers that multiply to 9 and add to 10. The numbers are 1 and 9.

   \[
   (x + 1)(x + 9) = 0
   \]

   Therefore, the solutions are:
   \[
   x = -1 \quad \text{or} \quad x = -9
   \]

---

3. \( x^2 + 5x - 14 = 0 \)

   To solve this, we apply factoring. We need two numbers that multiply to \(-14\) and add to 5. Unfortunately, this does not factor easily, so we will use the quadratic formula:

   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   where \( a = 1 \), \( b = 5 \), and \( c = -14 \).

   \[
   x = \frac{-5 \pm \sqrt{5^2 - 4(1)(-14)}}{2(1)}
   \]
   \[
   x = \frac{-5 \pm \sqrt{25 + 56}}{2}
   \]
   \[
   x = \frac{-5 \pm \sqrt{81}}{2}
   \]
   \[
   x = \frac{-5 \pm 9}{2}
   \]

   So, the solutions are:
   \[
   x = \frac{-5 + 9}{2} = 2 \quad \text{or} \quad x = \frac{-5 - 9}{2} = -7
   \]

---

5. \( x^2 + 7x = 4 \)

   First, rearrange the equation:
   \[
   x^2 + 7x - 4 = 0
   \]

   We will apply the quadratic formula since factoring isn't straightforward.

   \[
   x = \frac{-7 \pm \sqrt{7^2 - 4(1)(-4)}}{2(1)}
   \]
   \[
   x = \frac{-7 \pm \sqrt{49 + 16}}{2}
   \]
   \[
   x = \frac{-7 \pm \sqrt{65}}{2}
   \]

   Therefore, the solutions are:
   \[
   x = \frac{-7 \pm \sqrt{65}}{2}
   \]
   which gives two solutions in exact form.

---

7. \( 4x^2 - 4x + 1 = 0 \)

   This is a perfect square trinomial. We can write it as:
   \[
   (2x - 1)^2 = 0
   \]

   So, the solution is:
   \[
   x = \frac{1}{2}
   \]

---

9. \( 9x^2 - 72 = 0 \)

   Start by factoring:
   \[
   9(x^2 - 8) = 0
   \]

   Then:
   \[
   x^2 - 8 = 0
   \]
   \[
   x^2 = 8
   \]

   Taking the square root of both sides:
   \[
   x = \pm \sqrt{8} = \pm 2\sqrt{2}
   \]

---

Do you have any questions or want more details on any step? Here are 5 related problems for practice:

1. Solve \( x^2 - 6x + 9 = 0 \) using factoring.
2. Solve \( x^2 - 7x + 12 = 0 \) by completing the square.
3. Solve \( 3x^2 - 4x + 2 = 0 \) using the quadratic formula.
4. Factor and solve \( x^2 - 9x + 20 = 0 \).
5. Use the quadratic formula to solve \( x^2 + 3x - 10 = 0 \).

**Tip:** Always check if a quadratic can be factored before using the quadratic formula—it can save time!

Find the solutions of the quadratic equations: 1) x^2 + 10x + 9 = 0, 3) x^2 + 5x - 14 = 0, 5) x^2 + 7x = 4, 7) 4x^2 - 4x + 1 = 0, 9) 9x^2 - 72 = 0.

Learn to solve quadratic equations like x^2 + 10x + 9 = 0 using factoring, completing the square, and the quadratic formula. Detailed steps are provided for algebra students in Grades 8-10, covering various solution methods.

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