3.1d(2d+7)-6.2d-6.2d=19.53

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Solution for 3.1d(2d+7)-6.2d-6.2d=19.53 equation:


Simplifying
3.1d(2d + 7) + -6.2d + -6.2d = 19.53

Reorder the terms:
3.1d(7 + 2d) + -6.2d + -6.2d = 19.53
(7 * 3.1d + 2d * 3.1d) + -6.2d + -6.2d = 19.53
(21.7d + 6.2d2) + -6.2d + -6.2d = 19.53

Reorder the terms:
21.7d + -6.2d + -6.2d + 6.2d2 = 19.53

Combine like terms: 21.7d + -6.2d = 15.5d
15.5d + -6.2d + 6.2d2 = 19.53

Combine like terms: 15.5d + -6.2d = 9.3d
9.3d + 6.2d2 = 19.53

Solving
9.3d + 6.2d2 = 19.53

Solving for variable 'd'.

Reorder the terms:
-19.53 + 9.3d + 6.2d2 = 19.53 + -19.53

Combine like terms: 19.53 + -19.53 = 0.00
-19.53 + 9.3d + 6.2d2 = 0.00

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

Divide each side by '6.2'.
-3.15 + 1.5d + d2 = 0.0

Move the constant term to the right:

Add '3.15' to each side of the equation.
-3.15 + 1.5d + 3.15 + d2 = 0.0 + 3.15

Reorder the terms:
-3.15 + 3.15 + 1.5d + d2 = 0.0 + 3.15

Combine like terms: -3.15 + 3.15 = 0.00
0.00 + 1.5d + d2 = 0.0 + 3.15
1.5d + d2 = 0.0 + 3.15

Combine like terms: 0.0 + 3.15 = 3.15
1.5d + d2 = 3.15

The d term is 1.5d.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5d + 0.5625 + d2 = 3.15 + 0.5625

Reorder the terms:
0.5625 + 1.5d + d2 = 3.15 + 0.5625

Combine like terms: 3.15 + 0.5625 = 3.7125
0.5625 + 1.5d + d2 = 3.7125

Factor a perfect square on the left side:
(d + 0.75)(d + 0.75) = 3.7125

Calculate the square root of the right side: 1.926784887

Break this problem into two subproblems by setting 
(d + 0.75) equal to 1.926784887 and -1.926784887.


Subproblem 1
d + 0.75 = 1.926784887

Simplifying
d + 0.75 = 1.926784887

Reorder the terms:
0.75 + d = 1.926784887

Solving
0.75 + d = 1.926784887

Solving for variable 'd'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + d = 1.926784887 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + d = 1.926784887 + -0.75
d = 1.926784887 + -0.75

Combine like terms: 1.926784887 + -0.75 = 1.176784887
d = 1.176784887

Simplifying
d = 1.176784887


Subproblem 2
d + 0.75 = -1.926784887

Simplifying
d + 0.75 = -1.926784887

Reorder the terms:
0.75 + d = -1.926784887

Solving
0.75 + d = -1.926784887

Solving for variable 'd'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + d = -1.926784887 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + d = -1.926784887 + -0.75
d = -1.926784887 + -0.75

Combine like terms: -1.926784887 + -0.75 = -2.676784887
d = -2.676784887

Simplifying
d = -2.676784887


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {1.176784887, -2.676784887}

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