Can someone show me step by step on how to factor/solve this problem explaining the steps?
5.50 = (0.02x^3 + 5x) / x
expand the terms on the right:
5.50 = 0.02x^2/x + 5x/x
reduce the fractions:
5.50 = 0.02x + 5
subtract 5 from both sides:
0.50 = 0.02x
divide by 0.02 (or multiply by 50):
25 = x
To factor/solve the given problem, we want to simplify the equation and isolate the variable x. Here are the step-by-step instructions:
Step 1: Remove the denominator
Multiply both sides of the equation by x to eliminate the fraction:
5.50 * x = 0.02x^3 + 5x
Step 2: Arrange the equation
Rearrange the equation to have all the terms on one side, with the highest power of x first:
0.02x^3 + 5x - 5.50x = 0
Step 3: Combine like terms
Combine the constant terms and the x terms:
0.02x^3 + 5x - 5.50x = 0
0.02x^3 - 0.50x = 0
Step 4: Divide by common factors
Divide the entire equation by the common factor of 0.02:
(0.02x^3) / 0.02 - (0.50x) / 0.02 = 0 / 0.02
x^3 - 25x = 0
Step 5: Factor out x
Factor out the common factor, x:
x(x^2 - 25) = 0
Step 6: Solve for x
Set each factor equal to zero and solve for x:
x = 0 (from the factor x = 0)
x^2 - 25 = 0
Step 7: Solve the quadratic equation
To solve the quadratic equation, we can use the difference of squares:
x^2 - 25 = 0
(x + 5)(x - 5) = 0
Step 8: Final solutions
Set each factor equal to zero and solve for x:
x + 5 = 0 -> x = -5
x - 5 = 0 -> x = 5
So the solutions for the equation 5.50 = (0.02x^3 + 5x) / x are x = 0, x = -5, and x = 5.