d^2+6d-31=0

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Solution for d^2+6d-31=0 equation:


Simplifying
d2 + 6d + -31 = 0

Reorder the terms:
-31 + 6d + d2 = 0

Solving
-31 + 6d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 6d + 31 + d2 = 0 + 31

Reorder the terms:
-31 + 31 + 6d + d2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 6d + d2 = 0 + 31
6d + d2 = 0 + 31

Combine like terms: 0 + 31 = 31
6d + d2 = 31

The d term is 6d.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6d + 9 + d2 = 31 + 9

Reorder the terms:
9 + 6d + d2 = 31 + 9

Combine like terms: 31 + 9 = 40
9 + 6d + d2 = 40

Factor a perfect square on the left side:
(d + 3)(d + 3) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(d + 3) equal to 6.32455532 and -6.32455532.

Subproblem 1

d + 3 = 6.32455532 Simplifying d + 3 = 6.32455532 Reorder the terms: 3 + d = 6.32455532 Solving 3 + d = 6.32455532 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + d = 6.32455532 + -3 Combine like terms: 3 + -3 = 0 0 + d = 6.32455532 + -3 d = 6.32455532 + -3 Combine like terms: 6.32455532 + -3 = 3.32455532 d = 3.32455532 Simplifying d = 3.32455532

Subproblem 2

d + 3 = -6.32455532 Simplifying d + 3 = -6.32455532 Reorder the terms: 3 + d = -6.32455532 Solving 3 + d = -6.32455532 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + d = -6.32455532 + -3 Combine like terms: 3 + -3 = 0 0 + d = -6.32455532 + -3 d = -6.32455532 + -3 Combine like terms: -6.32455532 + -3 = -9.32455532 d = -9.32455532 Simplifying d = -9.32455532

Solution

The solution to the problem is based on the solutions from the subproblems. d = {3.32455532, -9.32455532}

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