4d^2-3d-3=0

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Solution for 4d^2-3d-3=0 equation: 


Simplifying
4d2 + -3d + -3 = 0

Reorder the terms:
-3 + -3d + 4d2 = 0

Solving
-3 + -3d + 4d2 = 0

Solving for variable 'd'.

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

Divide each side by '4'.
-0.75 + -0.75d + d2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -0.75d + 0.75 + d2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -0.75d + d2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -0.75d + d2 = 0 + 0.75
-0.75d + d2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-0.75d + d2 = 0.75

The d term is -0.75d.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75d + 0.140625 + d2 = 0.75 + 0.140625

Reorder the terms:
0.140625 + -0.75d + d2 = 0.75 + 0.140625

Combine like terms: 0.75 + 0.140625 = 0.890625
0.140625 + -0.75d + d2 = 0.890625

Factor a perfect square on the left side:
(d + -0.375)(d + -0.375) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(d + -0.375) equal to 0.943729304 and -0.943729304.


Subproblem 1
d + -0.375 = 0.943729304

Simplifying
d + -0.375 = 0.943729304

Reorder the terms:
-0.375 + d = 0.943729304

Solving
-0.375 + d = 0.943729304

Solving for variable 'd'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + d = 0.943729304 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + d = 0.943729304 + 0.375
d = 0.943729304 + 0.375

Combine like terms: 0.943729304 + 0.375 = 1.318729304
d = 1.318729304

Simplifying
d = 1.318729304


Subproblem 2
d + -0.375 = -0.943729304

Simplifying
d + -0.375 = -0.943729304

Reorder the terms:
-0.375 + d = -0.943729304

Solving
-0.375 + d = -0.943729304

Solving for variable 'd'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + d = -0.943729304 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + d = -0.943729304 + 0.375
d = -0.943729304 + 0.375

Combine like terms: -0.943729304 + 0.375 = -0.568729304
d = -0.568729304

Simplifying
d = -0.568729304


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {1.318729304, -0.568729304}

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