d^2-12d-6=0

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Solution for d^2-12d-6=0 equation:


Simplifying
d2 + -12d + -6 = 0

Reorder the terms:
-6 + -12d + d2 = 0

Solving
-6 + -12d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -12d + 6 + d2 = 0 + 6

Reorder the terms:
-6 + 6 + -12d + d2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -12d + d2 = 0 + 6
-12d + d2 = 0 + 6

Combine like terms: 0 + 6 = 6
-12d + d2 = 6

The d term is -12d.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12d + 36 + d2 = 6 + 36

Reorder the terms:
36 + -12d + d2 = 6 + 36

Combine like terms: 6 + 36 = 42
36 + -12d + d2 = 42

Factor a perfect square on the left side:
(d + -6)(d + -6) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(d + -6) equal to 6.480740698 and -6.480740698.

Subproblem 1

d + -6 = 6.480740698 Simplifying d + -6 = 6.480740698 Reorder the terms: -6 + d = 6.480740698 Solving -6 + d = 6.480740698 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + d = 6.480740698 + 6 Combine like terms: -6 + 6 = 0 0 + d = 6.480740698 + 6 d = 6.480740698 + 6 Combine like terms: 6.480740698 + 6 = 12.480740698 d = 12.480740698 Simplifying d = 12.480740698

Subproblem 2

d + -6 = -6.480740698 Simplifying d + -6 = -6.480740698 Reorder the terms: -6 + d = -6.480740698 Solving -6 + d = -6.480740698 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + d = -6.480740698 + 6 Combine like terms: -6 + 6 = 0 0 + d = -6.480740698 + 6 d = -6.480740698 + 6 Combine like terms: -6.480740698 + 6 = -0.480740698 d = -0.480740698 Simplifying d = -0.480740698

Solution

The solution to the problem is based on the solutions from the subproblems. d = {12.480740698, -0.480740698}

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