16d^2+6d-88=0

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Solution for 16d^2+6d-88=0 equation: 


Simplifying
16d2 + 6d + -88 = 0

Reorder the terms:
-88 + 6d + 16d2 = 0

Solving
-88 + 6d + 16d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-44 + 3d + 8d2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-44 + 3d + 8d2)' equal to zero and attempt to solve:

Simplifying
-44 + 3d + 8d2 = 0

Solving
-44 + 3d + 8d2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-5.5 + 0.375d + d2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 0.375d + 5.5 + d2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 0.375d + d2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 0.375d + d2 = 0 + 5.5
0.375d + d2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
0.375d + d2 = 5.5

The d term is 0.375d.  Take half its coefficient (0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
0.375d + 0.03515625 + d2 = 5.5 + 0.03515625

Reorder the terms:
0.03515625 + 0.375d + d2 = 5.5 + 0.03515625

Combine like terms: 5.5 + 0.03515625 = 5.53515625
0.03515625 + 0.375d + d2 = 5.53515625

Factor a perfect square on the left side:
(d + 0.1875)(d + 0.1875) = 5.53515625

Calculate the square root of the right side: 2.352691278

Break this problem into two subproblems by setting 
(d + 0.1875) equal to 2.352691278 and -2.352691278.


Subproblem 1
d + 0.1875 = 2.352691278

Simplifying
d + 0.1875 = 2.352691278

Reorder the terms:
0.1875 + d = 2.352691278

Solving
0.1875 + d = 2.352691278

Solving for variable 'd'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + d = 2.352691278 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + d = 2.352691278 + -0.1875
d = 2.352691278 + -0.1875

Combine like terms: 2.352691278 + -0.1875 = 2.165191278
d = 2.165191278

Simplifying
d = 2.165191278


Subproblem 2
d + 0.1875 = -2.352691278

Simplifying
d + 0.1875 = -2.352691278

Reorder the terms:
0.1875 + d = -2.352691278

Solving
0.1875 + d = -2.352691278

Solving for variable 'd'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + d = -2.352691278 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + d = -2.352691278 + -0.1875
d = -2.352691278 + -0.1875

Combine like terms: -2.352691278 + -0.1875 = -2.540191278
d = -2.540191278

Simplifying
d = -2.540191278


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {2.165191278, -2.540191278}
Solution
d = {2.165191278, -2.540191278}

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