Rihanna works in a coffee shop approximately nine miles from her apartment she bikes every day from her apartment to the coffee shop and then back to her apartment in the evening. however, on her way to work, she always stops halfway through to meet her best friend at a park. if the distance from apartment to the park is (5x 2) miles and the trip from the park to the coffee shop is (25x -8) miles long, then what is the value of x?

Given:
The total distance from the apartment to the coffee shop = 9 miles.
Distance from the apartment to the park = 5x².
Distance from the park to the coffee shop = 25x - 8.

Assume that all three locations lie in a straight line.
Then
5x² + 25x - 8 = 9
5x² + 25x - 17 = 0

Solve with the quadratic formula.
x = (1/10)[ -25 +/- √(25²+340 )] = 0.6064 or -5.6064.
Reject the negative answer.

Therefore,
Distance from the apartment to the park = 5x² = 1.839 miles.
Distance from the park to the coffee shop = 25x - 8 = 7.16 miles.

 x = 0.6064