To solve the equation \( x^2 + 5x = 0 \), we can use factoring. Let's go through the solution step-by-step:
1. Equation Simplification:
The given equation is:
[tex]\[
x^2 + 5x = 0
\][/tex]
2. Factoring:
Notice that there is a common factor of \( x \) in both terms. We can factor out \( x \) from the equation:
[tex]\[
x(x + 5) = 0
\][/tex]
3. Setting Factors to Zero:
According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. So, we set each factor to zero and solve for \( x \):
[tex]\[
x = 0 \quad \text{or} \quad x + 5 = 0
\][/tex]
4. Solving the Equations:
We solve these two equations separately:
For \( x = 0 \):
[tex]\[
x = 0
\][/tex]
For \( x + 5 = 0 \):
[tex]\[
x = -5
\][/tex]
So, the solutions to the equation \( x^2 + 5x = 0 \) are:
[tex]\[
x = 0 \quad \text{and} \quad x = -5
\][/tex]
