8000(d)=-5d^2+450d-1000

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Solution for 8000(d)=-5d^2+450d-1000 equation: 


Simplifying
8000(d) = -5d2 + 450d + -1000

Reorder the terms:
8000d = -1000 + 450d + -5d2

Solving
8000d = -1000 + 450d + -5d2

Solving for variable 'd'.

Reorder the terms:
1000 + 8000d + -450d + 5d2 = -1000 + 450d + -5d2 + 1000 + -450d + 5d2

Combine like terms: 8000d + -450d = 7550d
1000 + 7550d + 5d2 = -1000 + 450d + -5d2 + 1000 + -450d + 5d2

Reorder the terms:
1000 + 7550d + 5d2 = -1000 + 1000 + 450d + -450d + -5d2 + 5d2

Combine like terms: -1000 + 1000 = 0
1000 + 7550d + 5d2 = 0 + 450d + -450d + -5d2 + 5d2
1000 + 7550d + 5d2 = 450d + -450d + -5d2 + 5d2

Combine like terms: 450d + -450d = 0
1000 + 7550d + 5d2 = 0 + -5d2 + 5d2
1000 + 7550d + 5d2 = -5d2 + 5d2

Combine like terms: -5d2 + 5d2 = 0
1000 + 7550d + 5d2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(200 + 1510d + d2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(200 + 1510d + d2)' equal to zero and attempt to solve:

Simplifying
200 + 1510d + d2 = 0

Solving
200 + 1510d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-200' to each side of the equation.
200 + 1510d + -200 + d2 = 0 + -200

Reorder the terms:
200 + -200 + 1510d + d2 = 0 + -200

Combine like terms: 200 + -200 = 0
0 + 1510d + d2 = 0 + -200
1510d + d2 = 0 + -200

Combine like terms: 0 + -200 = -200
1510d + d2 = -200

The d term is 1510d.  Take half its coefficient (755).
Square it (570025) and add it to both sides.

Add '570025' to each side of the equation.
1510d + 570025 + d2 = -200 + 570025

Reorder the terms:
570025 + 1510d + d2 = -200 + 570025

Combine like terms: -200 + 570025 = 569825
570025 + 1510d + d2 = 569825

Factor a perfect square on the left side:
(d + 755)(d + 755) = 569825

Calculate the square root of the right side: 754.867538049

Break this problem into two subproblems by setting 
(d + 755) equal to 754.867538049 and -754.867538049.


Subproblem 1
d + 755 = 754.867538049

Simplifying
d + 755 = 754.867538049

Reorder the terms:
755 + d = 754.867538049

Solving
755 + d = 754.867538049

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-755' to each side of the equation.
755 + -755 + d = 754.867538049 + -755

Combine like terms: 755 + -755 = 0
0 + d = 754.867538049 + -755
d = 754.867538049 + -755

Combine like terms: 754.867538049 + -755 = -0.132461951
d = -0.132461951

Simplifying
d = -0.132461951


Subproblem 2
d + 755 = -754.867538049

Simplifying
d + 755 = -754.867538049

Reorder the terms:
755 + d = -754.867538049

Solving
755 + d = -754.867538049

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-755' to each side of the equation.
755 + -755 + d = -754.867538049 + -755

Combine like terms: 755 + -755 = 0
0 + d = -754.867538049 + -755
d = -754.867538049 + -755

Combine like terms: -754.867538049 + -755 = -1509.867538049
d = -1509.867538049

Simplifying
d = -1509.867538049


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {-0.132461951, -1509.867538049}
Solution
d = {-0.132461951, -1509.867538049}

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