-20d^2-82d+80=0

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Solution for -20d^2-82d+80=0 equation: 


Simplifying
-20d2 + -82d + 80 = 0

Reorder the terms:
80 + -82d + -20d2 = 0

Solving
80 + -82d + -20d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + -41d + -10d2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(40 + -41d + -10d2)' equal to zero and attempt to solve:

Simplifying
40 + -41d + -10d2 = 0

Solving
40 + -41d + -10d2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-4 + 4.1d + d2 = 0.0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 4.1d + 4 + d2 = 0.0 + 4

Reorder the terms:
-4 + 4 + 4.1d + d2 = 0.0 + 4

Combine like terms: -4 + 4 = 0
0 + 4.1d + d2 = 0.0 + 4
4.1d + d2 = 0.0 + 4

Combine like terms: 0.0 + 4 = 4
4.1d + d2 = 4

The d term is 4.1d.  Take half its coefficient (2.05).
Square it (4.2025) and add it to both sides.

Add '4.2025' to each side of the equation.
4.1d + 4.2025 + d2 = 4 + 4.2025

Reorder the terms:
4.2025 + 4.1d + d2 = 4 + 4.2025

Combine like terms: 4 + 4.2025 = 8.2025
4.2025 + 4.1d + d2 = 8.2025

Factor a perfect square on the left side:
(d + 2.05)(d + 2.05) = 8.2025

Calculate the square root of the right side: 2.864000698

Break this problem into two subproblems by setting 
(d + 2.05) equal to 2.864000698 and -2.864000698.


Subproblem 1
d + 2.05 = 2.864000698

Simplifying
d + 2.05 = 2.864000698

Reorder the terms:
2.05 + d = 2.864000698

Solving
2.05 + d = 2.864000698

Solving for variable 'd'.

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

Add '-2.05' to each side of the equation.
2.05 + -2.05 + d = 2.864000698 + -2.05

Combine like terms: 2.05 + -2.05 = 0.00
0.00 + d = 2.864000698 + -2.05
d = 2.864000698 + -2.05

Combine like terms: 2.864000698 + -2.05 = 0.814000698
d = 0.814000698

Simplifying
d = 0.814000698


Subproblem 2
d + 2.05 = -2.864000698

Simplifying
d + 2.05 = -2.864000698

Reorder the terms:
2.05 + d = -2.864000698

Solving
2.05 + d = -2.864000698

Solving for variable 'd'.

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

Add '-2.05' to each side of the equation.
2.05 + -2.05 + d = -2.864000698 + -2.05

Combine like terms: 2.05 + -2.05 = 0.00
0.00 + d = -2.864000698 + -2.05
d = -2.864000698 + -2.05

Combine like terms: -2.864000698 + -2.05 = -4.914000698
d = -4.914000698

Simplifying
d = -4.914000698


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.814000698, -4.914000698}
Solution
d = {0.814000698, -4.914000698}

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