Ariel is trying to determine if x = - 3 is a solution to the quadratic equation -3x* - 9x = 0.

Question

Which explanation demonstrates the correct reasoning? (1 point)
Yes, x = - 3 is a solution because substituting it back into the equation results in the following:
x Substituted
-3 - 3(-3)? - 9(-3) = 0 0=0
Evaluate True Statement?
True
No, 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)2 - 9(-3) = 0 54 ‡ 0 False
No, 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)* - 9(-3) = 0 -54 ¢ 0 False
Yes, x = —3 is a solution because substituting it back into the equation results in the following:
x Substituted
Evaluate True Statement?
-3 -3(-3) - 9(-3) = 0 54 = 0 True

Answer 1

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

The equation is: \[ -3x^2 - 9x = 0 \]

Substituting \( x = -3 \):

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

Calculating:

• First, compute \((-3)^2 = 9\).
• Then, compute \(-3(9) = -27\).
• Next, compute \(-9(-3) = 27\).

Putting it all together: \[ -27 + 27 = 0 \]

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

This is a true statement. Therefore, the correct explanation is:

Yes, \( x = -3 \) is a solution because substituting it back into the equation results in the following: \[ -3(-3)^2 - 9(-3) = 0 \quad \Rightarrow \quad 0 = 0 \quad \text{(True)} \]