Question

Ariel is trying to determine if x=−3 is a solution to the quadratic equation −3x2−9x=0 .

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 see if it holds true.

The original equation is:

\[
-3x^2 - 9x = 0
\]

Substituting \( x = -3 \):

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

Calculating \( (-3)^2 \):

\[
= -3(9) + 27
\]

Now simplify:

\[
= -27 + 27
\]

\[
= 0
\]

Since the left-hand side evaluates to 0, we have:

\[
0 = 0
\]

Thus, \( x = -3 \) is indeed a solution to the quadratic equation \( -3x^2 - 9x = 0 \).