solution sets of quadratic equations quick check
ariel is trying to determine if ( x = -3 ) is a solution to the quadratic equation ( -3x^2 - 9x = 0 ). 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
this table shows the evaluation of an expression for a specific value of ( x ), demonstrating the substitution, the resulting calculation, and the confirmation that the statement is true
| ( x ) | substituted | evaluate | true statement? |
| --- | --- | --- | --- |
| ( -3 ) | ( -3(-3)^2 - 9(-3) = 0 ) | ( 54 = 0 ) | true |
- yes, ( x = -3 ) is a solution because substituting it back into the equation results in the following:
this table shows the evaluation of an expression for a specific value of ( x ), demonstrating the substitution, the resulting calculation, and the confirmation that the statement is true
| ( 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
this table shows the evaluation of an expression for a specific value of ( x ), demonstrating the substitution, the resulting calculation, and the confirmation that the statement is true
| ( x ) | substituted | evaluate | true statement? |
| --- | --- | --- | --- |
| ( -3 ) | ( -3(-3)^2 - 9(-3) = 0 ) | ( -54
eq 0 ) | false |
- no, ( x = -3 ) is not a solution because substituting it back into the equation results in the following
this table shows the evaluation of an expression for a specific value of ( x ), demonstrating the substitution, the resulting calculation, and the confirmation that the statement is true
| ( x ) | substituted | evaluate | true statement? |
| --- | --- | --- | --- |
| ( -3 ) | ( -3(-3)^2 - 9(-3) = 0 ) | ( 54
eq 0 ) | false |

Question

solution sets of quadratic equations quick check
ariel is trying to determine if ( x = -3 ) is a solution to the quadratic equation ( -3x^2 - 9x = 0 ). 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
  this table shows the evaluation of an expression for a specific value of ( x ), demonstrating the substitution, the resulting calculation, and the confirmation that the statement is true
  | ( x ) | substituted | evaluate | true statement? |
  | --- | --- | --- | --- |
  | ( -3 ) | ( -3(-3)^2 - 9(-3) = 0 ) | ( 54 = 0 ) | true |
- yes, ( x = -3 ) is a solution because substituting it back into the equation results in the following:
  this table shows the evaluation of an expression for a specific value of ( x ), demonstrating the substitution, the resulting calculation, and the confirmation that the statement is true
  | ( 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
  this table shows the evaluation of an expression for a specific value of ( x ), demonstrating the substitution, the resulting calculation, and the confirmation that the statement is true
  | ( x ) | substituted | evaluate | true statement? |
  | --- | --- | --- | --- |
  | ( -3 ) | ( -3(-3)^2 - 9(-3) = 0 ) | ( -54
eq 0 ) | false |
- no, ( x = -3 ) is not a solution because substituting it back into the equation results in the following
  this table shows the evaluation of an expression for a specific value of ( x ), demonstrating the substitution, the resulting calculation, and the confirmation that the statement is true
  | ( x ) | substituted | evaluate | true statement? |
  | --- | --- | --- | --- |
  | ( -3 ) | ( -3(-3)^2 - 9(-3) = 0 ) | ( 54
eq 0 ) | false |

Accepted Answer

# Explanation:
## Step1: Substitute $ x = -3 $ into the equation $ -3x^2 - 9x = 0 $
First, calculate $ x^2 $ when $ x = -3 $: $ (-3)^2 = 9 $. Then substitute into the left - hand side of the equation:
$ -3\times(-3)^2-9\times(-3)=-3\times9 + 27 $
## Step2: Evaluate the expression
Calculate $ -3\times9=-27 $, then $ -27 + 27 = 0 $. So when $ x=-3 $, the left - hand side of the equation $ -3x^2 - 9x $ equals $ 0 $, which is equal to the right - hand side of the equation.

Now let's analyze each option:
- Option 1: The evaluation $ 54 = 0 $ is wrong. Because $ -3\times(-3)^2-9\times(-3)=-27 + 27 = 0
eq54 $.
- Option 2: When we substitute $ x = -3 $ into $ -3x^2-9x $, we have $ -3\times(-3)^2-9\times(-3)=-3\times9 + 27=-27 + 27 = 0 $, so $ 0 = 0 $ is a true statement. This means $ x=-3 $ is a solution.
- Option 3: The evaluation $ -54
eq0 $ is wrong. The correct result of $ -3\times(-3)^2-9\times(-3) $ is $ 0 $, not $ -54 $.
- Option 4: The evaluation $ 54
eq0 $ is wrong. The correct result of $ -3\times(-3)^2-9\times(-3) $ is $ 0 $, not $ 54 $.

# Answer:
Yes, $ x=-3 $ is a solution because substituting it back into the equation results in the following:

This table shows the evaluation of an expression for a specific value of $ x $, demonstrating the substitution, the resulting calculation, and the confirmation that the statement is true

| $ x $ | Substituted | Evaluate | True Statement? |
| ---- | ---- | ---- | ---- |
| $ -3 $ | $ -3(-3)^2 - 9(-3)=0 $ | $ 0 = 0 $ | True |

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QUESTION IMAGE

Question

Explanation:

Step1: Substitute \( x = -3 \) into the equation \( -3x^2 - 9x = 0 \)

Step2: Evaluate the expression

Answer: