the strategies listed, which is most appropriate for solving ?
square root property
zero product property
What are the square
Simplify the radical. Enter your answers in the boxes.
The solutions are

Ask by Morgan Turnbull. in the United States

Jan 23,2025

Question

the strategies listed, which is most appropriate for solving ?
square root property
zero product property
What are the square
Simplify the radical. Enter your answers in the boxes.
The solutions are

Ask by Morgan Turnbull. in the United States

Jan 23,2025

UpStudy AI · Accepted Answer

To solve the quadratic equation $$ q^{2} - 10q = 20 $$, let's follow the appropriate steps and fill in the solutions accordingly.

### 1. **Choose the Appropriate Strategy**

Given the equation $$ q^{2} - 10q = 20 $$, the **best strategy** to solve this is **completing the square**, which is closely related to the **square root property**. This method is more suitable here than the zero product property because the equation isn't initially factored.

### 2. **Solve the Equation by Completing the Square**

Let's solve the equation step by step:

1. **Start with the original equation:**
   $$
   q^2 - 10q = 20
   $$

2. **Move the constant term to the other side:**
   $$
   q^2 - 10q - 20 = 0 \quad \text{(Alternatively, keep the equation as } q^2 - 10q = 20 \text{)}
   $$

3. **Complete the square:**
   - Take half of the coefficient of $$ q $$: $$ \frac{-10}{2} = -5 $$.
   - Square it: $$ (-5)^2 = 25 $$.
   - Add 25 to both sides to complete the square:
     $$
     q^2 - 10q + 25 = 20 + 25
     $$
     $$
     (q - 5)^2 = 45
     $$

4. **Apply the square root property:**
   $$
   q - 5 = \pm \sqrt{45}
   $$

5. **Simplify the radical:**
   $$
   \sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}
   $$

6. **Solve for $$ q $$:**
   $$
   q = 5 \pm 3\sqrt{5}
   $$

### 3. **Enter the Solutions in the Boxes**

The solutions can be expressed as:
$$
\boxed{5 \pm 3\sqrt{5}}
$$

So, filling in the blanks:
- First box: **5**
- Second box: **3√5**

**Final Answer:**
$$
q = \boxed{5} \pm \boxed{3\sqrt{5}}
$$
The solutions are $$ 5 \pm 3\sqrt{5} $$.

the strategies listed, which is most appropriate for solving ?
square root property
zero product property
What are the square
Simplify the radical. Enter your answers in the boxes.
The solutions are

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