d^2+0.3275d-0.249=0

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Solution for d^2+0.3275d-0.249=0 equation:


Simplifying
d2 + 0.3275d + -0.249 = 0

Reorder the terms:
-0.249 + 0.3275d + d2 = 0

Solving
-0.249 + 0.3275d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '0.249' to each side of the equation.
-0.249 + 0.3275d + 0.249 + d2 = 0 + 0.249

Reorder the terms:
-0.249 + 0.249 + 0.3275d + d2 = 0 + 0.249

Combine like terms: -0.249 + 0.249 = 0.000
0.000 + 0.3275d + d2 = 0 + 0.249
0.3275d + d2 = 0 + 0.249

Combine like terms: 0 + 0.249 = 0.249
0.3275d + d2 = 0.249

The d term is 0.3275d.  Take half its coefficient (0.16375).
Square it (0.0268140625) and add it to both sides.

Add '0.0268140625' to each side of the equation.
0.3275d + 0.0268140625 + d2 = 0.249 + 0.0268140625

Reorder the terms:
0.0268140625 + 0.3275d + d2 = 0.249 + 0.0268140625

Combine like terms: 0.249 + 0.0268140625 = 0.2758140625
0.0268140625 + 0.3275d + d2 = 0.2758140625

Factor a perfect square on the left side:
(d + 0.16375)(d + 0.16375) = 0.2758140625

Calculate the square root of the right side: 0.525180029

Break this problem into two subproblems by setting 
(d + 0.16375) equal to 0.525180029 and -0.525180029.


Subproblem 1
d + 0.16375 = 0.525180029

Simplifying
d + 0.16375 = 0.525180029

Reorder the terms:
0.16375 + d = 0.525180029

Solving
0.16375 + d = 0.525180029

Solving for variable 'd'.

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

Add '-0.16375' to each side of the equation.
0.16375 + -0.16375 + d = 0.525180029 + -0.16375

Combine like terms: 0.16375 + -0.16375 = 0.00000
0.00000 + d = 0.525180029 + -0.16375
d = 0.525180029 + -0.16375

Combine like terms: 0.525180029 + -0.16375 = 0.361430029
d = 0.361430029

Simplifying
d = 0.361430029


Subproblem 2
d + 0.16375 = -0.525180029

Simplifying
d + 0.16375 = -0.525180029

Reorder the terms:
0.16375 + d = -0.525180029

Solving
0.16375 + d = -0.525180029

Solving for variable 'd'.

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

Add '-0.16375' to each side of the equation.
0.16375 + -0.16375 + d = -0.525180029 + -0.16375

Combine like terms: 0.16375 + -0.16375 = 0.00000
0.00000 + d = -0.525180029 + -0.16375
d = -0.525180029 + -0.16375

Combine like terms: -0.525180029 + -0.16375 = -0.688930029
d = -0.688930029

Simplifying
d = -0.688930029


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.361430029, -0.688930029}

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