d^2+0.16054d-0.178=0

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Solution for d^2+0.16054d-0.178=0 equation:


Simplifying
d2 + 0.16054d + -0.178 = 0

Reorder the terms:
-0.178 + 0.16054d + d2 = 0

Solving
-0.178 + 0.16054d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '0.178' to each side of the equation.
-0.178 + 0.16054d + 0.178 + d2 = 0 + 0.178

Reorder the terms:
-0.178 + 0.178 + 0.16054d + d2 = 0 + 0.178

Combine like terms: -0.178 + 0.178 = 0.000
0.000 + 0.16054d + d2 = 0 + 0.178
0.16054d + d2 = 0 + 0.178

Combine like terms: 0 + 0.178 = 0.178
0.16054d + d2 = 0.178

The d term is 0.16054d.  Take half its coefficient (0.08027).
Square it (0.0064432729) and add it to both sides.

Add '0.0064432729' to each side of the equation.
0.16054d + 0.0064432729 + d2 = 0.178 + 0.0064432729

Reorder the terms:
0.0064432729 + 0.16054d + d2 = 0.178 + 0.0064432729

Combine like terms: 0.178 + 0.0064432729 = 0.1844432729
0.0064432729 + 0.16054d + d2 = 0.1844432729

Factor a perfect square on the left side:
(d + 0.08027)(d + 0.08027) = 0.1844432729

Calculate the square root of the right side: 0.429468594

Break this problem into two subproblems by setting 
(d + 0.08027) equal to 0.429468594 and -0.429468594.


Subproblem 1
d + 0.08027 = 0.429468594

Simplifying
d + 0.08027 = 0.429468594

Reorder the terms:
0.08027 + d = 0.429468594

Solving
0.08027 + d = 0.429468594

Solving for variable 'd'.

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

Add '-0.08027' to each side of the equation.
0.08027 + -0.08027 + d = 0.429468594 + -0.08027

Combine like terms: 0.08027 + -0.08027 = 0.00000
0.00000 + d = 0.429468594 + -0.08027
d = 0.429468594 + -0.08027

Combine like terms: 0.429468594 + -0.08027 = 0.349198594
d = 0.349198594

Simplifying
d = 0.349198594


Subproblem 2
d + 0.08027 = -0.429468594

Simplifying
d + 0.08027 = -0.429468594

Reorder the terms:
0.08027 + d = -0.429468594

Solving
0.08027 + d = -0.429468594

Solving for variable 'd'.

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

Add '-0.08027' to each side of the equation.
0.08027 + -0.08027 + d = -0.429468594 + -0.08027

Combine like terms: 0.08027 + -0.08027 = 0.00000
0.00000 + d = -0.429468594 + -0.08027
d = -0.429468594 + -0.08027

Combine like terms: -0.429468594 + -0.08027 = -0.509738594
d = -0.509738594

Simplifying
d = -0.509738594


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.349198594, -0.509738594}

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