0.592=4.25*d+6.8*d^2

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Solution for 0.592=4.25*d+6.8*d^2 equation: 


Simplifying
0.592 = 4.25d + 6.8d2

Solving
0.592 = 4.25d + 6.8d2

Solving for variable 'd'.

Reorder the terms:
0.592 + -4.25d + -6.8d2 = 4.25d + -4.25d + 6.8d2 + -6.8d2

Combine like terms: 4.25d + -4.25d = 0.00
0.592 + -4.25d + -6.8d2 = 0.00 + 6.8d2 + -6.8d2
0.592 + -4.25d + -6.8d2 = 6.8d2 + -6.8d2

Combine like terms: 6.8d2 + -6.8d2 = 0.0
0.592 + -4.25d + -6.8d2 = 0.0

Begin completing the square.  Divide all terms by
-6.8 the coefficient of the squared term: 

Divide each side by '-6.8'.
-0.08705882353 + 0.625d + d2 = 0

Move the constant term to the right:

Add '0.08705882353' to each side of the equation.
-0.08705882353 + 0.625d + 0.08705882353 + d2 = 0 + 0.08705882353

Reorder the terms:
-0.08705882353 + 0.08705882353 + 0.625d + d2 = 0 + 0.08705882353

Combine like terms: -0.08705882353 + 0.08705882353 = 0.00000000000
0.00000000000 + 0.625d + d2 = 0 + 0.08705882353
0.625d + d2 = 0 + 0.08705882353

Combine like terms: 0 + 0.08705882353 = 0.08705882353
0.625d + d2 = 0.08705882353

The d term is 0.625d.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625d + 0.09765625 + d2 = 0.08705882353 + 0.09765625

Reorder the terms:
0.09765625 + 0.625d + d2 = 0.08705882353 + 0.09765625

Combine like terms: 0.08705882353 + 0.09765625 = 0.18471507353
0.09765625 + 0.625d + d2 = 0.18471507353

Factor a perfect square on the left side:
(d + 0.3125)(d + 0.3125) = 0.18471507353

Calculate the square root of the right side: 0.429784915

Break this problem into two subproblems by setting 
(d + 0.3125) equal to 0.429784915 and -0.429784915.


Subproblem 1
d + 0.3125 = 0.429784915

Simplifying
d + 0.3125 = 0.429784915

Reorder the terms:
0.3125 + d = 0.429784915

Solving
0.3125 + d = 0.429784915

Solving for variable 'd'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + d = 0.429784915 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + d = 0.429784915 + -0.3125
d = 0.429784915 + -0.3125

Combine like terms: 0.429784915 + -0.3125 = 0.117284915
d = 0.117284915

Simplifying
d = 0.117284915


Subproblem 2
d + 0.3125 = -0.429784915

Simplifying
d + 0.3125 = -0.429784915

Reorder the terms:
0.3125 + d = -0.429784915

Solving
0.3125 + d = -0.429784915

Solving for variable 'd'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + d = -0.429784915 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + d = -0.429784915 + -0.3125
d = -0.429784915 + -0.3125

Combine like terms: -0.429784915 + -0.3125 = -0.742284915
d = -0.742284915

Simplifying
d = -0.742284915


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.117284915, -0.742284915}

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