Ariel is trying to determine if x=−3

Question

𝑥
=
−
3
is a solution to the quadratic equation −3x2−9x=0
−
3
𝑥
2
−
9
𝑥
=
0
. Which explanation demonstrates the correct reasoning?(1 point)
Responses

No, x=−3
𝑥
=
−
3
is not a solution because substituting it back into the equation results in the following:

x Substituted Evaluate True Statement?
−3
−
3
−3(−3)2−9(−3)=0
−
3
(
−
3
)
2
−
9
(
−
3
)
=
0
54≠0
54
≠
0
False
No, x equals negative 3 is not a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 54 does not equal 0 False

Yes, x=−3
𝑥
=
−
3
is a solution because substituting it back into the equation results in the following:

x Substituted Evaluate True Statement?
−3
−
3
−3(−3)2−9(−3)=0
−
3
(
−
3
)
2
−
9

Answer 1

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

1. Substitute \( x = -3 \):

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

2. Calculate \( (-3)^2 \):

   \[ = -3(9) - 9(-3) \]

3. Calculate the products:

   \[ = -27 + 27 \]

4. Now, simplify:

   \[ -27 + 27 = 0 \]

Since the left side of the equation equals \( 0 \), we have \( 0 = 0 \), which is a true statement.

Thus, the correct conclusion is:

Yes, \( x = -3 \) is a solution because substituting it back into the equation results in a true statement.

The preferred phrasing would look like this:

"Yes, \( x = -3 \) is a solution because substituting it back into the equation results in the following:

\[ -3(-3)^2 - 9(-3) = 0 \implies -27 + 27 = 0 \implies 0 = 0 \]

This demonstrates that \( x = -3 \) satisfies the equation."