Question

Ariel is trying to determine it x = -3 is a solution to the quadratic equation -3x^2 - 9x = 0

Answer 1

To determine if \( x = -3 \) is a solution to the quadratic equation \( -3x^2 - 9x = 0 \), we can substitute \( x = -3 \) into the equation and see if it holds true.

Let's substitute \( x = -3 \):

\[
-3(-3)^2 - 9(-3) = 0
\]

Calculating each term:

1. Calculate \((-3)^2\):
\[
(-3)^2 = 9
\]

2. Now substitute this back into the equation:
\[
-3(9) - 9(-3)
\]

3. Compute \( -3(9) \):
\[
-27
\]

4. Compute \( -9(-3) \):
\[
27
\]

Now, combine these results:

\[
-27 + 27 = 0
\]

Since the left side of the equation equals to 0, we have:

\[
0 = 0
\]

Thus, \( x = -3 \) is indeed a solution to the quadratic equation \( -3x^2 - 9x = 0 \).