To solve the given equation, we will start by solving for d:
900d+8100 - 900d / d^2 + 9d = 32.5
We can simplify the equation by cancelling out the common term "900d":
8100 / d^2 + 9d = 32.5
Now, we can multiply both sides of the equation by (d^2 + 9d) to clear the denominator:
8100 = 32.5(d^2 + 9d)
Divide by 32.5:
d^2 + 9d = 8100 / 32.5
d^2 + 9d = 249.23
Rearranging to solve for d:
d^2 + 9d - 249.23 = 0
Now, we can use the quadratic formula to solve for the value of d. The formula is:
d = (-b ± √(b^2 - 4ac)) / (2a)
Where a = 1, b = 9, and c = -249.23:
d = (-9 ± √(9^2 - 4*1*(-249.23))) / (2*1)
d = (-9 ± √(81 + 996.92)) / 2
d = (-9 ± √1077.92) / 2
d = (-9 ± 32.8) / 2
We have two possible solutions:
d₁ = (-9 + 32.8) / 2 = 23.8 / 2 = 11.9 days
d₂ = (-9 - 32.8) / 2 = -41.8 / 2 = -20.9 days
Since the number of days cannot be negative, we discard the second solution:
So, Ahmed expected to complete the house in approximately 11.9 days.
