4d^2-8d-88=0

Solution for 4d^2-8d-88=0 equation:

Simplifying
4d2 + -8d + -88 = 0

Reorder the terms:
-88 + -8d + 4d2 = 0

Solving
-88 + -8d + 4d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-22 + -2d + d2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-22 + -2d + d2)' equal to zero and attempt to solve:

Simplifying
-22 + -2d + d2 = 0

Solving
-22 + -2d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -2d + 22 + d2 = 0 + 22

Reorder the terms:
-22 + 22 + -2d + d2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -2d + d2 = 0 + 22
-2d + d2 = 0 + 22

Combine like terms: 0 + 22 = 22
-2d + d2 = 22

The d term is -2d.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2d + 1 + d2 = 22 + 1

Reorder the terms:
1 + -2d + d2 = 22 + 1

Combine like terms: 22 + 1 = 23
1 + -2d + d2 = 23

Factor a perfect square on the left side:
(d + -1)(d + -1) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(d + -1) equal to 4.795831523 and -4.795831523.

Subproblem 1
d + -1 = 4.795831523

Simplifying
d + -1 = 4.795831523

Reorder the terms:
-1 + d = 4.795831523

Solving
-1 + d = 4.795831523

Solving for variable 'd'.

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

Add '1' to each side of the equation.
-1 + 1 + d = 4.795831523 + 1

Combine like terms: -1 + 1 = 0
0 + d = 4.795831523 + 1
d = 4.795831523 + 1

Combine like terms: 4.795831523 + 1 = 5.795831523
d = 5.795831523

Simplifying
d = 5.795831523

Subproblem 2
d + -1 = -4.795831523

Simplifying
d + -1 = -4.795831523

Reorder the terms:
-1 + d = -4.795831523

Solving
-1 + d = -4.795831523

Solving for variable 'd'.

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

Add '1' to each side of the equation.
-1 + 1 + d = -4.795831523 + 1

Combine like terms: -1 + 1 = 0
0 + d = -4.795831523 + 1
d = -4.795831523 + 1

Combine like terms: -4.795831523 + 1 = -3.795831523
d = -3.795831523

Simplifying
d = -3.795831523

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {5.795831523, -3.795831523}
Solution
d = {5.795831523, -3.795831523}