d^2+0.403d-0.2845=0

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Solution for d^2+0.403d-0.2845=0 equation:


Simplifying
d2 + 0.403d + -0.2845 = 0

Reorder the terms:
-0.2845 + 0.403d + d2 = 0

Solving
-0.2845 + 0.403d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '0.2845' to each side of the equation.
-0.2845 + 0.403d + 0.2845 + d2 = 0 + 0.2845

Reorder the terms:
-0.2845 + 0.2845 + 0.403d + d2 = 0 + 0.2845

Combine like terms: -0.2845 + 0.2845 = 0.0000
0.0000 + 0.403d + d2 = 0 + 0.2845
0.403d + d2 = 0 + 0.2845

Combine like terms: 0 + 0.2845 = 0.2845
0.403d + d2 = 0.2845

The d term is 0.403d.  Take half its coefficient (0.2015).
Square it (0.04060225) and add it to both sides.

Add '0.04060225' to each side of the equation.
0.403d + 0.04060225 + d2 = 0.2845 + 0.04060225

Reorder the terms:
0.04060225 + 0.403d + d2 = 0.2845 + 0.04060225

Combine like terms: 0.2845 + 0.04060225 = 0.32510225
0.04060225 + 0.403d + d2 = 0.32510225

Factor a perfect square on the left side:
(d + 0.2015)(d + 0.2015) = 0.32510225

Calculate the square root of the right side: 0.570177385

Break this problem into two subproblems by setting 
(d + 0.2015) equal to 0.570177385 and -0.570177385.


Subproblem 1
d + 0.2015 = 0.570177385

Simplifying
d + 0.2015 = 0.570177385

Reorder the terms:
0.2015 + d = 0.570177385

Solving
0.2015 + d = 0.570177385

Solving for variable 'd'.

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

Add '-0.2015' to each side of the equation.
0.2015 + -0.2015 + d = 0.570177385 + -0.2015

Combine like terms: 0.2015 + -0.2015 = 0.0000
0.0000 + d = 0.570177385 + -0.2015
d = 0.570177385 + -0.2015

Combine like terms: 0.570177385 + -0.2015 = 0.368677385
d = 0.368677385

Simplifying
d = 0.368677385


Subproblem 2
d + 0.2015 = -0.570177385

Simplifying
d + 0.2015 = -0.570177385

Reorder the terms:
0.2015 + d = -0.570177385

Solving
0.2015 + d = -0.570177385

Solving for variable 'd'.

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

Add '-0.2015' to each side of the equation.
0.2015 + -0.2015 + d = -0.570177385 + -0.2015

Combine like terms: 0.2015 + -0.2015 = 0.0000
0.0000 + d = -0.570177385 + -0.2015
d = -0.570177385 + -0.2015

Combine like terms: -0.570177385 + -0.2015 = -0.771677385
d = -0.771677385

Simplifying
d = -0.771677385


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.368677385, -0.771677385}

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