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

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
−

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 simplify.

Substituting \( x = -3 \):

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

Now, calculate each term:

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

2. Now substitute that back into the equation: \[ -3(9) - 9(-3) = 0 \]

3. Now calculate: \[ -27 + 27 = 0 \]

So, we have: \[ 0 = 0 \]

This indicates that when substituting \( x = -3 \) into the equation, it results in a true statement.

Therefore, the correct conclusion is:

Yes, \( x = -3 \) is a solution to the quadratic equation \( -3x^2 - 9x = 0 \) because substituting it back into the equation results in the equation holding true:

\[ -27 + 27 = 0 \]

Let me know if you need further assistance!