i have no clue how to solve this!! the problem is...
20x^3 - 125x = 0
(twenty x to the third power minus onehundredandtwentyfive x equals zero)
it asks to find all the solutions for the equation. please help!!
To solve the equation 20x^3 - 125x = 0, follow these steps:
Step 1: Factor out the greatest common factor from each term.
In this case, the terms 20 and 125 have a common factor of 5 and the variables x have a common factor of x. So, we can factor out 5x:
5x(4x^2 - 25) = 0
Step 2: Solve each factor separately.
The equation 5x = 0 implies that x = 0.
Now, consider the factor (4x^2 - 25) = 0. This is a quadratic equation that can be factored further.
Step 3: Factor the quadratic equation (4x^2 - 25) = 0.
You can rewrite (4x^2 - 25) = 0 as (2x)^2 - 5^2 = 0. This is a difference of squares, so you can factor the equation:
(2x - 5)(2x + 5) = 0
Step 4: Solve the factors.
Setting each factor to equal zero, you get:
2x - 5 = 0 --> 2x = 5 --> x = 5/2
2x + 5 = 0 --> 2x = -5 --> x = -5/2
Therefore, the solutions to the equation 20x^3 - 125x = 0 are x = 0, x = 5/2, and x = -5/2.