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?

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 holds true.

Starting with the equation: $$-3x^2-9x=0$$

Substituting $x=-3$: $$-3(-3{)}^2-9(-3)=0$$

Calculating $(-3{)}^2$: $$-3(9)-9(-3)=0$$

Now simplifying: $$-27+27=0$$

This simplifies to: $$0=0$$

Since this statement is true, it demonstrates that $x=-3$ is indeed a solution to the equation $-3x^2-9x=0$.

Therefore, the correct reasoning is that substituting $-3$ into the equation yields a true statement, confirming that $x=-3$ is a solution.