Question
Solve by applying the zero product property. \[ m^{2}+4 m=21 \] If there is more than one solution, separate the answers with commas.
Ask by Wyatt Robbins. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solutions are \( m = -7 \) and \( m = 3 \).
Solution
To solve the quadratic equation \( m^{2} + 4m = 21 \) using the **zero product property**, follow these steps:
1. **Move all terms to one side of the equation:**
\[
m^{2} + 4m - 21 = 0
\]
2. **Factor the quadratic expression:**
We need two numbers that multiply to \(-21\) and add up to \(4\). Those numbers are \(7\) and \(-3\).
\[
(m + 7)(m - 3) = 0
\]
3. **Apply the zero product property:**
If the product of two factors is zero, then at least one of the factors must be zero.
\[
m + 7 = 0 \quad \text{or} \quad m - 3 = 0
\]
4. **Solve for \( m \):**
- For \( m + 7 = 0 \):
\[
m = -7
\]
- For \( m - 3 = 0 \):
\[
m = 3
\]
**Solutions:** \(-7, 3\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
First, we need to rearrange the equation into the standard form of a quadratic equation. Start by moving 21 to the left side: \[ m^2 + 4m - 21 = 0. \] Now, we can factor the quadratic expression. We look for two numbers that multiply to -21 (the constant term) and add up to 4 (the coefficient of the middle term). Those two numbers are 7 and -3. Therefore, we can factor the equation as: \[ (m + 7)(m - 3) = 0. \] By the zero product property, we set each factor equal to zero: 1. \( m + 7 = 0 \) → \( m = -7 \) 2. \( m - 3 = 0 \) → \( m = 3 \) Thus, the solutions are: \[ m = -7, 3. \]
