-6d^2+9d-2=0

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Solution for -6d^2+9d-2=0 equation:


Simplifying
-6d2 + 9d + -2 = 0

Reorder the terms:
-2 + 9d + -6d2 = 0

Solving
-2 + 9d + -6d2 = 0

Solving for variable 'd'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.3333333333 + -1.5d + d2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1.5d + -0.3333333333 + d2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1.5d + d2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1.5d + d2 = 0 + -0.3333333333
-1.5d + d2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1.5d + d2 = -0.3333333333

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 = -0.3333333333 + 0.5625

Reorder the terms:
0.5625 + -1.5d + d2 = -0.3333333333 + 0.5625

Combine like terms: -0.3333333333 + 0.5625 = 0.2291666667
0.5625 + -1.5d + d2 = 0.2291666667

Factor a perfect square on the left side:
(d + -0.75)(d + -0.75) = 0.2291666667

Calculate the square root of the right side: 0.478713554

Break this problem into two subproblems by setting 
(d + -0.75) equal to 0.478713554 and -0.478713554.

Subproblem 1

d + -0.75 = 0.478713554 Simplifying d + -0.75 = 0.478713554 Reorder the terms: -0.75 + d = 0.478713554 Solving -0.75 + d = 0.478713554 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 = 0.478713554 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + d = 0.478713554 + 0.75 d = 0.478713554 + 0.75 Combine like terms: 0.478713554 + 0.75 = 1.228713554 d = 1.228713554 Simplifying d = 1.228713554

Subproblem 2

d + -0.75 = -0.478713554 Simplifying d + -0.75 = -0.478713554 Reorder the terms: -0.75 + d = -0.478713554 Solving -0.75 + d = -0.478713554 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 = -0.478713554 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + d = -0.478713554 + 0.75 d = -0.478713554 + 0.75 Combine like terms: -0.478713554 + 0.75 = 0.271286446 d = 0.271286446 Simplifying d = 0.271286446

Solution

The solution to the problem is based on the solutions from the subproblems. d = {1.228713554, 0.271286446}

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