-9d-8=-4(d+2)5d

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Solution for -9d-8=-4(d+2)5d equation: 


Simplifying
-9d + -8 = -4(d + 2) * 5d

Reorder the terms:
-8 + -9d = -4(d + 2) * 5d

Reorder the terms:
-8 + -9d = -4(2 + d) * 5d

Reorder the terms for easier multiplication:
-8 + -9d = -4 * 5d(2 + d)

Multiply -4 * 5
-8 + -9d = -20d(2 + d)
-8 + -9d = (2 * -20d + d * -20d)
-8 + -9d = (-40d + -20d2)

Solving
-8 + -9d = -40d + -20d2

Solving for variable 'd'.

Combine like terms: -9d + 40d = 31d
-8 + 31d + 20d2 = -40d + -20d2 + 40d + 20d2

Reorder the terms:
-8 + 31d + 20d2 = -40d + 40d + -20d2 + 20d2

Combine like terms: -40d + 40d = 0
-8 + 31d + 20d2 = 0 + -20d2 + 20d2
-8 + 31d + 20d2 = -20d2 + 20d2

Combine like terms: -20d2 + 20d2 = 0
-8 + 31d + 20d2 = 0

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

Divide each side by '20'.
-0.4 + 1.55d + d2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 1.55d + 0.4 + d2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 1.55d + d2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 1.55d + d2 = 0 + 0.4
1.55d + d2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
1.55d + d2 = 0.4

The d term is 1.55d.  Take half its coefficient (0.775).
Square it (0.600625) and add it to both sides.

Add '0.600625' to each side of the equation.
1.55d + 0.600625 + d2 = 0.4 + 0.600625

Reorder the terms:
0.600625 + 1.55d + d2 = 0.4 + 0.600625

Combine like terms: 0.4 + 0.600625 = 1.000625
0.600625 + 1.55d + d2 = 1.000625

Factor a perfect square on the left side:
(d + 0.775)(d + 0.775) = 1.000625

Calculate the square root of the right side: 1.000312451

Break this problem into two subproblems by setting 
(d + 0.775) equal to 1.000312451 and -1.000312451.


Subproblem 1
d + 0.775 = 1.000312451

Simplifying
d + 0.775 = 1.000312451

Reorder the terms:
0.775 + d = 1.000312451

Solving
0.775 + d = 1.000312451

Solving for variable 'd'.

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

Add '-0.775' to each side of the equation.
0.775 + -0.775 + d = 1.000312451 + -0.775

Combine like terms: 0.775 + -0.775 = 0.000
0.000 + d = 1.000312451 + -0.775
d = 1.000312451 + -0.775

Combine like terms: 1.000312451 + -0.775 = 0.225312451
d = 0.225312451

Simplifying
d = 0.225312451


Subproblem 2
d + 0.775 = -1.000312451

Simplifying
d + 0.775 = -1.000312451

Reorder the terms:
0.775 + d = -1.000312451

Solving
0.775 + d = -1.000312451

Solving for variable 'd'.

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

Add '-0.775' to each side of the equation.
0.775 + -0.775 + d = -1.000312451 + -0.775

Combine like terms: 0.775 + -0.775 = 0.000
0.000 + d = -1.000312451 + -0.775
d = -1.000312451 + -0.775

Combine like terms: -1.000312451 + -0.775 = -1.775312451
d = -1.775312451

Simplifying
d = -1.775312451


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.225312451, -1.775312451}

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