Sure! Let's determine whether [tex]\( x = -3 \)[/tex] is a solution to the equation [tex]\( x^2 - 3x = 0 \)[/tex].
Here's a step-by-step method to verify the solution:
1. Substitute [tex]\( x = -3 \)[/tex] into the equation [tex]\( x^2 - 3x = 0 \)[/tex]:
[tex]\[
(-3)^2 - 3(-3) = 0
\][/tex]
2. Calculate each term separately:
- First term: [tex]\( (-3)^2 \)[/tex]:
[tex]\[
(-3)^2 = 9
\][/tex]
- Second term: [tex]\( -3(-3) \)[/tex]:
[tex]\[
-3(-3) = 9
\][/tex]
3. Combine the terms:
[tex]\[
9 + 9 = 18
\][/tex]
4. Check if the left side equals the right side:
[tex]\[
18 \neq 0
\][/tex]
Since substituting [tex]\( x = -3 \)[/tex] into [tex]\( x^2 - 3x = 0 \)[/tex] does not satisfy the equation, [tex]\( x = -3 \)[/tex] is not a solution.
Now, let's find the correct solutions to the equation [tex]\( x^2 - 3x = 0 \)[/tex] using factorization:
1. Factorize the equation:
[tex]\[
x^2 - 3x = 0
\][/tex]
[tex]\[
x(x - 3) = 0
\][/tex]
2. Set each factor to zero to find the solutions:
[tex]\[
x = 0 \quad \text{or} \quad x - 3 = 0
\][/tex]
3. Solve each equation:
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
x = 0
\][/tex]
- For [tex]\( x - 3 = 0 \)[/tex]:
[tex]\[
x = 3
\][/tex]
So, the solutions to the equation [tex]\( x^2 - 3x = 0 \)[/tex] are [tex]\( x = 0 \)[/tex] and [tex]\( x = 3 \)[/tex].
In conclusion, [tex]\( x = -3 \)[/tex] is not a solution to the equation [tex]\( x^2 - 3x = 0 \)[/tex]. The correct solutions are [tex]\( x = 0 \)[/tex] and [tex]\( x = 3 \)[/tex].
