d^2-3d+2=8d+3

Solution for d^2-3d+2=8d+3 equation:

Simplifying
d2 + -3d + 2 = 8d + 3

Reorder the terms:
2 + -3d + d2 = 8d + 3

Reorder the terms:
2 + -3d + d2 = 3 + 8d

Solving
2 + -3d + d2 = 3 + 8d

Solving for variable 'd'.

Reorder the terms:
2 + -3 + -3d + -8d + d2 = 3 + 8d + -3 + -8d

Combine like terms: 2 + -3 = -1
-1 + -3d + -8d + d2 = 3 + 8d + -3 + -8d

Combine like terms: -3d + -8d = -11d
-1 + -11d + d2 = 3 + 8d + -3 + -8d

Reorder the terms:
-1 + -11d + d2 = 3 + -3 + 8d + -8d

Combine like terms: 3 + -3 = 0
-1 + -11d + d2 = 0 + 8d + -8d
-1 + -11d + d2 = 8d + -8d

Combine like terms: 8d + -8d = 0
-1 + -11d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -11d + 1 + d2 = 0 + 1

Reorder the terms:
-1 + 1 + -11d + d2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -11d + d2 = 0 + 1
-11d + d2 = 0 + 1

Combine like terms: 0 + 1 = 1
-11d + d2 = 1

The d term is -11d.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11d + 30.25 + d2 = 1 + 30.25

Reorder the terms:
30.25 + -11d + d2 = 1 + 30.25

Combine like terms: 1 + 30.25 = 31.25
30.25 + -11d + d2 = 31.25

Factor a perfect square on the left side:
(d + -5.5)(d + -5.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(d + -5.5) equal to 5.590169944 and -5.590169944.

Subproblem 1
d + -5.5 = 5.590169944

Simplifying
d + -5.5 = 5.590169944

Reorder the terms:
-5.5 + d = 5.590169944

Solving
-5.5 + d = 5.590169944

Solving for variable 'd'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + d = 5.590169944 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + d = 5.590169944 + 5.5
d = 5.590169944 + 5.5

Combine like terms: 5.590169944 + 5.5 = 11.090169944
d = 11.090169944

Simplifying
d = 11.090169944

Subproblem 2
d + -5.5 = -5.590169944

Simplifying
d + -5.5 = -5.590169944

Reorder the terms:
-5.5 + d = -5.590169944

Solving
-5.5 + d = -5.590169944

Solving for variable 'd'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + d = -5.590169944 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + d = -5.590169944 + 5.5
d = -5.590169944 + 5.5

Combine like terms: -5.590169944 + 5.5 = -0.090169944
d = -0.090169944

Simplifying
d = -0.090169944

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {11.090169944, -0.090169944}