2d^2+24d-94=0

Solution for 2d^2+24d-94=0 equation:

Simplifying
2d2 + 24d + -94 = 0

Reorder the terms:
-94 + 24d + 2d2 = 0

Solving
-94 + 24d + 2d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-47 + 12d + d2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-47 + 12d + d2)' equal to zero and attempt to solve:

Simplifying
-47 + 12d + d2 = 0

Solving
-47 + 12d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + 12d + 47 + d2 = 0 + 47

Reorder the terms:
-47 + 47 + 12d + d2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + 12d + d2 = 0 + 47
12d + d2 = 0 + 47

Combine like terms: 0 + 47 = 47
12d + d2 = 47

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 = 47 + 36

Reorder the terms:
36 + 12d + d2 = 47 + 36

Combine like terms: 47 + 36 = 83
36 + 12d + d2 = 83

Factor a perfect square on the left side:
(d + 6)(d + 6) = 83

Calculate the square root of the right side: 9.110433579

Break this problem into two subproblems by setting 
(d + 6) equal to 9.110433579 and -9.110433579.

Subproblem 1
d + 6 = 9.110433579

Simplifying
d + 6 = 9.110433579

Reorder the terms:
6 + d = 9.110433579

Solving
6 + d = 9.110433579

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 = 9.110433579 + -6

Combine like terms: 6 + -6 = 0
0 + d = 9.110433579 + -6
d = 9.110433579 + -6

Combine like terms: 9.110433579 + -6 = 3.110433579
d = 3.110433579

Simplifying
d = 3.110433579

Subproblem 2
d + 6 = -9.110433579

Simplifying
d + 6 = -9.110433579

Reorder the terms:
6 + d = -9.110433579

Solving
6 + d = -9.110433579

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 = -9.110433579 + -6

Combine like terms: 6 + -6 = 0
0 + d = -9.110433579 + -6
d = -9.110433579 + -6

Combine like terms: -9.110433579 + -6 = -15.110433579
d = -15.110433579

Simplifying
d = -15.110433579

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {3.110433579, -15.110433579}
Solution
d = {3.110433579, -15.110433579}