Question

Ariel is trying to determine if
x
=
−
3
is a solution to the quadratic equation
−
3
x
2
−
9
x
=
0
. Whichexplanation 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 Evaluate True Statement?
−3 −3(−3)2 − 9(−3) = 0 0 = 0 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)2 − 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)2 − 9(−3) = 0 54 = 0 True
A)

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 evaluate it.

Starting with the equation:

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

Calculating each part:

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

2. Then multiply by \(-3\):
\[
-3(9) = -27
\]

3. Now calculate \( -9(-3) \):
\[
-9(-3) = 27
\]

Putting it all together:

\[
-27 + 27 = 0
\]

This simplifies to:

\[
0 = 0
\]

Since we have a true statement, \( x = -3 \) is indeed a solution to the equation.

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

So, the correct choice is the first one:
**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)² − 9(−3) = 0 0 = 0 True**