To solve the equation [tex]\(x^2 + 7x = 0\)[/tex], we can follow these steps:
1. Factor the equation:
Given [tex]\(x^2 + 7x = 0\)[/tex], we can factor out the common term [tex]\(x\)[/tex].
[tex]\[
x(x + 7) = 0
\][/tex]
2. Use the Zero Product Property:
The Zero Product Property states that if the product of two factors is zero, at least one of the factors has to be zero. Therefore, we set each factor equal to zero:
[tex]\[
x = 0
\][/tex]
and
[tex]\[
x + 7 = 0
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
We solve each equation separately.
First, solving [tex]\(x = 0\)[/tex]:
[tex]\[
x = 0
\][/tex]
Second, solving [tex]\(x + 7 = 0\)[/tex]:
[tex]\[
x + 7 = 0
\][/tex]
Subtract 7 from both sides:
[tex]\[
x = -7
\][/tex]
Therefore, the solutions to the equation [tex]\(x^2 + 7x = 0\)[/tex] are:
[tex]\[
x = 0 \quad \text{and} \quad x = -7
\][/tex]
So, the solutions are [tex]\(x = -7\)[/tex] and [tex]\(x = 0\)[/tex].
