Answer:
a = -4
b = 3
c = 6
Step-by-step explanation:
x^2 + 8x = 38
We take the coefficient of the x term
Divide by 2 and then square it
8/2 =4
4^2 = 16
Add 16 to both sides
x^2 +8x + 16 = 38 + 16
x^2 +8x +16 = 54
Take b/2 and use it in the the (x+b/2)^2
(x+4)^2 = 54
Take the square root of each side
sqrt((x+4)^2) = ± sqrt(54)
x+4 = ± sqrt(54)
Subtract 4 from each side
x+4-4 = -4 ± sqrt(54)
x = -4 ± sqrt(54)
Simplify the square root
x = -4 ± sqrt(9*6)
x = -4 ± sqrt(9) sqrt(6)
x = -4 ± 3 sqrt(6)
Answer: the width of the uniform path is 9 meters.
Step-by-step explanation:
Let x represent the width of the uniform path.
A pool measuring 18 meters by 22 meters is surrounded by a path of uniform width. It means that the combined length of the pool and the uniform path is (18 + 2x) meters and the combined width of the pool and the uniform path is (22 + 2x) meters.
If the area of the pool and the path combined is 1440 square meters, it means that
(18 + 2x)(22 + 2x) = 1440
396 + 36x + 44x + 4x² = 1440
4x² + 80x + 396 - 1440 = 0
4x² + 80x - 1044 = 0
Dividing both sides of the equation by 4, it becomes
x² + 20x - 261 = 0
x² + 29x - 9x - 261 = 0
x(x + 29) - 9(x + 29) = 0
x - 9 = 0 or x + 29 = 0
x = 9 or x = 29
Since the width cannot be negative, then x = 9 meters
