D^2+1.5D-30=0

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Solution for D^2+1.5D-30=0 equation: 


Simplifying
D2 + 1.5D + -30 = 0

Reorder the terms:
-30 + 1.5D + D2 = 0

Solving
-30 + 1.5D + D2 = 0

Solving for variable 'D'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 1.5D + 30 + D2 = 0 + 30

Reorder the terms:
-30 + 30 + 1.5D + D2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 1.5D + D2 = 0 + 30
1.5D + D2 = 0 + 30

Combine like terms: 0 + 30 = 30
1.5D + D2 = 30

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 = 30 + 0.5625

Reorder the terms:
0.5625 + 1.5D + D2 = 30 + 0.5625

Combine like terms: 30 + 0.5625 = 30.5625
0.5625 + 1.5D + D2 = 30.5625

Factor a perfect square on the left side:
(D + 0.75)(D + 0.75) = 30.5625

Calculate the square root of the right side: 5.528336097

Break this problem into two subproblems by setting 
(D + 0.75) equal to 5.528336097 and -5.528336097.


Subproblem 1
D + 0.75 = 5.528336097

Simplifying
D + 0.75 = 5.528336097

Reorder the terms:
0.75 + D = 5.528336097

Solving
0.75 + D = 5.528336097

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 = 5.528336097 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + D = 5.528336097 + -0.75
D = 5.528336097 + -0.75

Combine like terms: 5.528336097 + -0.75 = 4.778336097
D = 4.778336097

Simplifying
D = 4.778336097


Subproblem 2
D + 0.75 = -5.528336097

Simplifying
D + 0.75 = -5.528336097

Reorder the terms:
0.75 + D = -5.528336097

Solving
0.75 + D = -5.528336097

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 = -5.528336097 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + D = -5.528336097 + -0.75
D = -5.528336097 + -0.75

Combine like terms: -5.528336097 + -0.75 = -6.278336097
D = -6.278336097

Simplifying
D = -6.278336097


Solution
The solution to the problem is based on the solutions
from the subproblems.
D = {4.778336097, -6.278336097}

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