Question

Solve the equation for all values of xx.
2, x, left parenthesis, x, squared, minus, 100, right parenthesis, left parenthesis, 9, x, squared, minus, 25, right parenthesis, equals, 0
2x(x
2
−100)(9x
2
−25)=0

Answer 1

To solve the equation \( 2x(x^2 - 100)(9x^2 - 25) = 0 \), we can set each factor equal to zero individually.

1. **Set the first factor to zero**:
\[
2x = 0
\]
Solving for \( x \):
\[
x = 0
\]

2. **Set the second factor to zero**:
\[
x^2 - 100 = 0
\]
Solving for \( x \):
\[
x^2 = 100
\]
Taking the square root of both sides, we get:
\[
x = 10 \quad \text{or} \quad x = -10
\]

3. **Set the third factor to zero**:
\[
9x^2 - 25 = 0
\]
Solving for \( x \):
\[
9x^2 = 25
\]
\[
x^2 = \frac{25}{9}
\]
Taking the square root of both sides, we get:
\[
x = \frac{5}{3} \quad \text{or} \quad x = -\frac{5}{3}
\]

Now, we can combine all the solutions:

The solutions to the equation \( 2x(x^2 - 100)(9x^2 - 25) = 0 \) are:
\[
x = 0, \quad x = 10, \quad x = -10, \quad x = \frac{5}{3}, \quad x = -\frac{5}{3}
\]

Thus, the complete set of solutions is:
\[
\boxed{0, 10, -10, \frac{5}{3}, -\frac{5}{3}}
\]