88.9d^2+7903d-356000=0

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Solution for 88.9d^2+7903d-356000=0 equation: 


Simplifying
88.9d2 + 7903d + -356000 = 0

Reorder the terms:
-356000 + 7903d + 88.9d2 = 0

Solving
-356000 + 7903d + 88.9d2 = 0

Solving for variable 'd'.

Begin completing the square.  Divide all terms by
88.9 the coefficient of the squared term: 

Divide each side by '88.9'.
-4004.499438 + 88.8976378d + d2 = 0

Move the constant term to the right:

Add '4004.499438' to each side of the equation.
-4004.499438 + 88.8976378d + 4004.499438 + d2 = 0 + 4004.499438

Reorder the terms:
-4004.499438 + 4004.499438 + 88.8976378d + d2 = 0 + 4004.499438

Combine like terms: -4004.499438 + 4004.499438 = 0.000000
0.000000 + 88.8976378d + d2 = 0 + 4004.499438
88.8976378d + d2 = 0 + 4004.499438

Combine like terms: 0 + 4004.499438 = 4004.499438
88.8976378d + d2 = 4004.499438

The d term is 88.8976378d.  Take half its coefficient (44.4488189).
Square it (1975.697502) and add it to both sides.

Add '1975.697502' to each side of the equation.
88.8976378d + 1975.697502 + d2 = 4004.499438 + 1975.697502

Reorder the terms:
1975.697502 + 88.8976378d + d2 = 4004.499438 + 1975.697502

Combine like terms: 4004.499438 + 1975.697502 = 5980.19694
1975.697502 + 88.8976378d + d2 = 5980.19694

Factor a perfect square on the left side:
(d + 44.4488189)(d + 44.4488189) = 5980.19694

Calculate the square root of the right side: 77.331733073

Break this problem into two subproblems by setting 
(d + 44.4488189) equal to 77.331733073 and -77.331733073.


Subproblem 1
d + 44.4488189 = 77.331733073

Simplifying
d + 44.4488189 = 77.331733073

Reorder the terms:
44.4488189 + d = 77.331733073

Solving
44.4488189 + d = 77.331733073

Solving for variable 'd'.

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

Add '-44.4488189' to each side of the equation.
44.4488189 + -44.4488189 + d = 77.331733073 + -44.4488189

Combine like terms: 44.4488189 + -44.4488189 = 0.0000000
0.0000000 + d = 77.331733073 + -44.4488189
d = 77.331733073 + -44.4488189

Combine like terms: 77.331733073 + -44.4488189 = 32.882914173
d = 32.882914173

Simplifying
d = 32.882914173


Subproblem 2
d + 44.4488189 = -77.331733073

Simplifying
d + 44.4488189 = -77.331733073

Reorder the terms:
44.4488189 + d = -77.331733073

Solving
44.4488189 + d = -77.331733073

Solving for variable 'd'.

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

Add '-44.4488189' to each side of the equation.
44.4488189 + -44.4488189 + d = -77.331733073 + -44.4488189

Combine like terms: 44.4488189 + -44.4488189 = 0.0000000
0.0000000 + d = -77.331733073 + -44.4488189
d = -77.331733073 + -44.4488189

Combine like terms: -77.331733073 + -44.4488189 = -121.780551973
d = -121.780551973

Simplifying
d = -121.780551973


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {32.882914173, -121.780551973}

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