To find the solutions to the equation [tex]\( x(x + 8) = 0 \)[/tex], we can apply the zero product property. The zero product property states that if the product of two numbers is zero, at least one of the numbers must be zero. Thus, we need to set each factor in the equation equal to zero and solve for [tex]\( x \)[/tex].
Starting with the given equation:
[tex]\[ x(x + 8) = 0 \][/tex]
We can break it into two separate equations:
1. [tex]\( x = 0 \)[/tex]
2. [tex]\( x + 8 = 0 \)[/tex]
### Step-by-step solution:
1. Solve the first equation:
[tex]\[ x = 0 \][/tex]
This is already simplified, so one solution to the equation is:
[tex]\[ x = 0 \][/tex]
2. Solve the second equation:
[tex]\[ x + 8 = 0 \][/tex]
To isolate [tex]\( x \)[/tex], subtract 8 from both sides:
[tex]\[ x = -8 \][/tex]
Thus, the other solution to the equation is:
[tex]\[ x = -8 \][/tex]
### Conclusion:
The solutions to the equation [tex]\( x(x + 8) = 0 \)[/tex] are:
[tex]\[ x = 0 \][/tex]
and
[tex]\[ x = -8 \][/tex]
