Solve the quadratic equation by completing the square and applying the square root property.
202 + 8v + 20 = 0

Let's solve the quadratic equation \( 202 + 8v + 20 = 0 \) by completing the square and applying the square root property.

### Step 1: Simplify the equation
First, simplify the constant terms:

\[
202 + 20 + 8v = 0
\]

\[
222 + 8v = 0
\]

Now subtract 222 from both sides:

\[
8v = -222
\]

### Step 2: Solve for \( v \)
Divide both sides by 8:

\[
v = \frac{-222}{8}
\]

\[
v = -27.75
\]

So the solution is \( v = -27.75 \).

Would you like to discuss this process in more detail, or do you have any other questions?

Here are 5 related questions:
1. How does completing the square typically work for more complex quadratic equations?
2. How would you handle an equation with larger coefficients?
3. Can you solve this equation graphically, and what would the graph look like?
4. What if this equation had complex roots? How would the solution change?
5. How do you apply the quadratic formula for equations like this?

**Tip:** Always double-check your simplifications to avoid errors in final solutions!

Solve the quadratic equation by completing the square and applying the square root property: 202 + 8v + 20 = 0

Explore how to solve the quadratic equation 202 + 8v + 20 = 0 step-by-step using the completing the square method and square root property. This solution highlights key algebra concepts and formulas, suitable for Grades 9-10 students.

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