3d^2-43d-12=0

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Solution for 3d^2-43d-12=0 equation:


Simplifying
3d2 + -43d + -12 = 0

Reorder the terms:
-12 + -43d + 3d2 = 0

Solving
-12 + -43d + 3d2 = 0

Solving for variable 'd'.

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

Divide each side by '3'.
-4 + -14.33333333d + d2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -14.33333333d + 4 + d2 = 0 + 4

Reorder the terms:
-4 + 4 + -14.33333333d + d2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -14.33333333d + d2 = 0 + 4
-14.33333333d + d2 = 0 + 4

Combine like terms: 0 + 4 = 4
-14.33333333d + d2 = 4

The d term is -14.33333333d.  Take half its coefficient (-7.166666665).
Square it (51.36111109) and add it to both sides.

Add '51.36111109' to each side of the equation.
-14.33333333d + 51.36111109 + d2 = 4 + 51.36111109

Reorder the terms:
51.36111109 + -14.33333333d + d2 = 4 + 51.36111109

Combine like terms: 4 + 51.36111109 = 55.36111109
51.36111109 + -14.33333333d + d2 = 55.36111109

Factor a perfect square on the left side:
(d + -7.166666665)(d + -7.166666665) = 55.36111109

Calculate the square root of the right side: 7.44050476

Break this problem into two subproblems by setting 
(d + -7.166666665) equal to 7.44050476 and -7.44050476.

Subproblem 1

d + -7.166666665 = 7.44050476 Simplifying d + -7.166666665 = 7.44050476 Reorder the terms: -7.166666665 + d = 7.44050476 Solving -7.166666665 + d = 7.44050476 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '7.166666665' to each side of the equation. -7.166666665 + 7.166666665 + d = 7.44050476 + 7.166666665 Combine like terms: -7.166666665 + 7.166666665 = 0.000000000 0.000000000 + d = 7.44050476 + 7.166666665 d = 7.44050476 + 7.166666665 Combine like terms: 7.44050476 + 7.166666665 = 14.607171425 d = 14.607171425 Simplifying d = 14.607171425

Subproblem 2

d + -7.166666665 = -7.44050476 Simplifying d + -7.166666665 = -7.44050476 Reorder the terms: -7.166666665 + d = -7.44050476 Solving -7.166666665 + d = -7.44050476 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '7.166666665' to each side of the equation. -7.166666665 + 7.166666665 + d = -7.44050476 + 7.166666665 Combine like terms: -7.166666665 + 7.166666665 = 0.000000000 0.000000000 + d = -7.44050476 + 7.166666665 d = -7.44050476 + 7.166666665 Combine like terms: -7.44050476 + 7.166666665 = -0.273838095 d = -0.273838095 Simplifying d = -0.273838095

Solution

The solution to the problem is based on the solutions from the subproblems. d = {14.607171425, -0.273838095}

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