d^2+16d-11=0

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Solution for d^2+16d-11=0 equation: 


Simplifying
d2 + 16d + -11 = 0

Reorder the terms:
-11 + 16d + d2 = 0

Solving
-11 + 16d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 16d + 11 + d2 = 0 + 11

Reorder the terms:
-11 + 11 + 16d + d2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 16d + d2 = 0 + 11
16d + d2 = 0 + 11

Combine like terms: 0 + 11 = 11
16d + d2 = 11

The d term is 16d.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16d + 64 + d2 = 11 + 64

Reorder the terms:
64 + 16d + d2 = 11 + 64

Combine like terms: 11 + 64 = 75
64 + 16d + d2 = 75

Factor a perfect square on the left side:
(d + 8)(d + 8) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(d + 8) equal to 8.660254038 and -8.660254038.


Subproblem 1
d + 8 = 8.660254038

Simplifying
d + 8 = 8.660254038

Reorder the terms:
8 + d = 8.660254038

Solving
8 + d = 8.660254038

Solving for variable 'd'.

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

Add '-8' to each side of the equation.
8 + -8 + d = 8.660254038 + -8

Combine like terms: 8 + -8 = 0
0 + d = 8.660254038 + -8
d = 8.660254038 + -8

Combine like terms: 8.660254038 + -8 = 0.660254038
d = 0.660254038

Simplifying
d = 0.660254038


Subproblem 2
d + 8 = -8.660254038

Simplifying
d + 8 = -8.660254038

Reorder the terms:
8 + d = -8.660254038

Solving
8 + d = -8.660254038

Solving for variable 'd'.

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

Add '-8' to each side of the equation.
8 + -8 + d = -8.660254038 + -8

Combine like terms: 8 + -8 = 0
0 + d = -8.660254038 + -8
d = -8.660254038 + -8

Combine like terms: -8.660254038 + -8 = -16.660254038
d = -16.660254038

Simplifying
d = -16.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.660254038, -16.660254038}

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