Solve the following equation by factoring.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There is no solution.

Question

Solve the following equation by factoring.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is

(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There is no solution.

UpStudy AI · Accepted Answer

To solve the quadratic equation $$ z^{2} + 2z - 15 = 0 $$ by factoring, follow these steps:

1. **Find two numbers that multiply to $$-15$$ and add up to $$2$$.**
   
   - The numbers $$5$$ and $$-3$$ satisfy this condition because:
     $$
     5 \times (-3) = -15 \quad \text{and} \quad 5 + (-3) = 2
     $$

2. **Factor the quadratic equation using these numbers:**
   $$
   z^{2} + 2z - 15 = (z + 5)(z - 3) = 0
   $$

3. **Set each factor equal to zero and solve for $$z$$:**
   
   - $$z + 5 = 0 \Rightarrow z = -5$$
   - $$z - 3 = 0 \Rightarrow z = 3$$

Therefore, the solution set is $$\{-5, 3\}$$.

**Answer:**  
**A. The solution set is $$\{-5, 3\}$$**
The solution set is $$\{-5, 3\}$$.

Solve the following equation by factoring.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There is no solution.

Upstudy AI Solution

Answer

Solution

Mind Expander

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Latest Algebra Questions

Solve the following equation by factoring. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no solution.

Upstudy AI Solution

Answer

Solution

Mind Expander

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Latest Algebra Questions

Solve the following equation by factoring.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There is no solution.