6d^2+21d-30d-35=0

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Solution for 6d^2+21d-30d-35=0 equation:


Simplifying
6d2 + 21d + -30d + -35 = 0

Reorder the terms:
-35 + 21d + -30d + 6d2 = 0

Combine like terms: 21d + -30d = -9d
-35 + -9d + 6d2 = 0

Solving
-35 + -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'.
-5.833333333 + -1.5d + d2 = 0

Move the constant term to the right:

Add '5.833333333' to each side of the equation.
-5.833333333 + -1.5d + 5.833333333 + d2 = 0 + 5.833333333

Reorder the terms:
-5.833333333 + 5.833333333 + -1.5d + d2 = 0 + 5.833333333

Combine like terms: -5.833333333 + 5.833333333 = 0.000000000
0.000000000 + -1.5d + d2 = 0 + 5.833333333
-1.5d + d2 = 0 + 5.833333333

Combine like terms: 0 + 5.833333333 = 5.833333333
-1.5d + d2 = 5.833333333

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 = 5.833333333 + 0.5625

Reorder the terms:
0.5625 + -1.5d + d2 = 5.833333333 + 0.5625

Combine like terms: 5.833333333 + 0.5625 = 6.395833333
0.5625 + -1.5d + d2 = 6.395833333

Factor a perfect square on the left side:
(d + -0.75)(d + -0.75) = 6.395833333

Calculate the square root of the right side: 2.528998484

Break this problem into two subproblems by setting 
(d + -0.75) equal to 2.528998484 and -2.528998484.

Subproblem 1

d + -0.75 = 2.528998484 Simplifying d + -0.75 = 2.528998484 Reorder the terms: -0.75 + d = 2.528998484 Solving -0.75 + d = 2.528998484 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 = 2.528998484 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + d = 2.528998484 + 0.75 d = 2.528998484 + 0.75 Combine like terms: 2.528998484 + 0.75 = 3.278998484 d = 3.278998484 Simplifying d = 3.278998484

Subproblem 2

d + -0.75 = -2.528998484 Simplifying d + -0.75 = -2.528998484 Reorder the terms: -0.75 + d = -2.528998484 Solving -0.75 + d = -2.528998484 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 = -2.528998484 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + d = -2.528998484 + 0.75 d = -2.528998484 + 0.75 Combine like terms: -2.528998484 + 0.75 = -1.778998484 d = -1.778998484 Simplifying d = -1.778998484

Solution

The solution to the problem is based on the solutions from the subproblems. d = {3.278998484, -1.778998484}

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