8d^2-64d+32=0

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Solution for 8d^2-64d+32=0 equation: 


Simplifying
8d2 + -64d + 32 = 0

Reorder the terms:
32 + -64d + 8d2 = 0

Solving
32 + -64d + 8d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '8'.
8(4 + -8d + d2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(4 + -8d + d2)' equal to zero and attempt to solve:

Simplifying
4 + -8d + d2 = 0

Solving
4 + -8d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -8d + -4 + d2 = 0 + -4

Reorder the terms:
4 + -4 + -8d + d2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -8d + d2 = 0 + -4
-8d + d2 = 0 + -4

Combine like terms: 0 + -4 = -4
-8d + d2 = -4

The d term is -8d.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8d + 16 + d2 = -4 + 16

Reorder the terms:
16 + -8d + d2 = -4 + 16

Combine like terms: -4 + 16 = 12
16 + -8d + d2 = 12

Factor a perfect square on the left side:
(d + -4)(d + -4) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(d + -4) equal to 3.464101615 and -3.464101615.


Subproblem 1
d + -4 = 3.464101615

Simplifying
d + -4 = 3.464101615

Reorder the terms:
-4 + d = 3.464101615

Solving
-4 + d = 3.464101615

Solving for variable 'd'.

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

Add '4' to each side of the equation.
-4 + 4 + d = 3.464101615 + 4

Combine like terms: -4 + 4 = 0
0 + d = 3.464101615 + 4
d = 3.464101615 + 4

Combine like terms: 3.464101615 + 4 = 7.464101615
d = 7.464101615

Simplifying
d = 7.464101615


Subproblem 2
d + -4 = -3.464101615

Simplifying
d + -4 = -3.464101615

Reorder the terms:
-4 + d = -3.464101615

Solving
-4 + d = -3.464101615

Solving for variable 'd'.

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

Add '4' to each side of the equation.
-4 + 4 + d = -3.464101615 + 4

Combine like terms: -4 + 4 = 0
0 + d = -3.464101615 + 4
d = -3.464101615 + 4

Combine like terms: -3.464101615 + 4 = 0.535898385
d = 0.535898385

Simplifying
d = 0.535898385


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {7.464101615, 0.535898385}
Solution
d = {7.464101615, 0.535898385}

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