-d^2-23d-50=0

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Solution for -d^2-23d-50=0 equation: 


Simplifying
-1d2 + -23d + -50 = 0

Reorder the terms:
-50 + -23d + -1d2 = 0

Solving
-50 + -23d + -1d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(50 + 23d + d2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(50 + 23d + d2)' equal to zero and attempt to solve:

Simplifying
50 + 23d + d2 = 0

Solving
50 + 23d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + 23d + -50 + d2 = 0 + -50

Reorder the terms:
50 + -50 + 23d + d2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + 23d + d2 = 0 + -50
23d + d2 = 0 + -50

Combine like terms: 0 + -50 = -50
23d + d2 = -50

The d term is 23d.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23d + 132.25 + d2 = -50 + 132.25

Reorder the terms:
132.25 + 23d + d2 = -50 + 132.25

Combine like terms: -50 + 132.25 = 82.25
132.25 + 23d + d2 = 82.25

Factor a perfect square on the left side:
(d + 11.5)(d + 11.5) = 82.25

Calculate the square root of the right side: 9.069178574

Break this problem into two subproblems by setting 
(d + 11.5) equal to 9.069178574 and -9.069178574.


Subproblem 1
d + 11.5 = 9.069178574

Simplifying
d + 11.5 = 9.069178574

Reorder the terms:
11.5 + d = 9.069178574

Solving
11.5 + d = 9.069178574

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-11.5' to each side of the equation.
11.5 + -11.5 + d = 9.069178574 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + d = 9.069178574 + -11.5
d = 9.069178574 + -11.5

Combine like terms: 9.069178574 + -11.5 = -2.430821426
d = -2.430821426

Simplifying
d = -2.430821426


Subproblem 2
d + 11.5 = -9.069178574

Simplifying
d + 11.5 = -9.069178574

Reorder the terms:
11.5 + d = -9.069178574

Solving
11.5 + d = -9.069178574

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-11.5' to each side of the equation.
11.5 + -11.5 + d = -9.069178574 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + d = -9.069178574 + -11.5
d = -9.069178574 + -11.5

Combine like terms: -9.069178574 + -11.5 = -20.569178574
d = -20.569178574

Simplifying
d = -20.569178574


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {-2.430821426, -20.569178574}
Solution
d = {-2.430821426, -20.569178574}

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