Question

Use factoring to solve the equation.
vsquaredminus8vminus20 ​= 0
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Part 1
The solution is vequals
  
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Answer 1

To solve the equation \( v^2 - 8v - 20 = 0 \) by factoring, we first need to find two numbers that multiply to \(-20\) (the constant term) and add up to \(-8\) (the coefficient of the \(v\) term).

The two numbers that work are \(-10\) and \(2\) because:

\[
-10 \times 2 = -20 \quad \text{(product)}
\]
\[
-10 + 2 = -8 \quad \text{(sum)}
\]

Now we can factor the quadratic equation:

\[
v^2 - 8v - 20 = (v - 10)(v + 2) = 0
\]

Next, we set each factor to zero:

1. \( v - 10 = 0 \) → \( v = 10 \)
2. \( v + 2 = 0 \) → \( v = -2 \)

Thus, the solutions to the equation are:

\[
v = 10 \quad \text{and} \quad v = -2
\]

So, the final answer is:
- The solutions are \( v = 10 \) and \( v = -2 \).