Question
Solve the equation using the zero-product property. \[ 2 x(x+5)=0 \]
Ask by Warner Grant. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are \( x = 0 \) or \( x = -5 \).
Solution
1. Begin with the equation:
\[
2x(x+5)=0
\]
2. Apply the zero-product property which states that if \(\,AB=0\), then either \(\,A=0\) or \(\,B=0\). Set each factor equal to zero:
\[
2x=0 \quad \text{or} \quad x+5=0
\]
3. Solve each equation separately:
- For \(\,2x=0\):
\[
x=0
\]
- For \(\,x+5=0\):
\[
x=-5
\]
4. The solutions are:
\[
x=0 \quad \text{or} \quad x=-5
\]
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Simplify this solution Bonus Knowledge
To solve the equation using the zero-product property, we need to set each factor equal to zero. Our equation is: \[ 2x(x + 5) = 0 \] First, notice that \( 2x = 0 \) gives us \( x = 0 \). Next, for the factor \( (x + 5) = 0 \), we get \( x = -5 \). So the solutions to the equation are: \[ x = 0 \quad \text{and} \quad x = -5 \] Now we can wrap it all up and say that the values of \( x \) that satisfy the original equation are \( 0 \) and \( -5 \).
