The area of a rectangular swimming pool is 10x2 – 19x – 15. The length of the pool is 5x + 3. What is the width of the pool?
To find the width of the pool, we need to divide the area of the pool by the length.
Area = Length x Width
10x^2 – 19x – 15 = (5x + 3) x Width
10x^2 – 19x – 15 = 5x^2 + 15x
5x^2 - 34x - 15 = 0
Now we can solve this quadratic equation using the quadratic formula:
x = (-(-34) ± √((-34)^2 - 4*5*-15)) / 2*5
x = (34 ± √(1156 + 300)) / 10
x = (34 ± √1456) / 10
x = (34 ± 38.15) / 10
x = 7.61 or x = -0.61
Since the width of a pool cannot be negative, the width of the pool is 7.61.