Question

Find the solutions to 6x2 - 54x=0.
Check all that apply.
x=0
x= 6
x=-9
x=9

Answer 1

To solve the equation \(6x^2 - 54x = 0\), we can factor it.

1. Factor out the common term:
\[
6x(x - 9) = 0
\]

2. Set each factor to zero:
\[
6x = 0 \quad \text{or} \quad x - 9 = 0
\]

From \(6x = 0\):
\[
x = 0
\]

From \(x - 9 = 0\):
\[
x = 9
\]

Thus, the solutions to the equation \(6x^2 - 54x = 0\) are:
\[
x = 0 \quad \text{and} \quad x = 9
\]

Now, let's check the provided options:
- \(x = 0\) (Valid)
- \(x = 6\) (Not a solution)
- \(x = -9\) (Not a solution)
- \(x = 9\) (Valid)

The valid solutions from the options provided are:
- \(x = 0\)
- \(x = 9\)