d^2-4d-24=0

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Solution for d^2-4d-24=0 equation: 


Simplifying
d2 + -4d + -24 = 0

Reorder the terms:
-24 + -4d + d2 = 0

Solving
-24 + -4d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -4d + 24 + d2 = 0 + 24

Reorder the terms:
-24 + 24 + -4d + d2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -4d + d2 = 0 + 24
-4d + d2 = 0 + 24

Combine like terms: 0 + 24 = 24
-4d + d2 = 24

The d term is -4d.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4d + 4 + d2 = 24 + 4

Reorder the terms:
4 + -4d + d2 = 24 + 4

Combine like terms: 24 + 4 = 28
4 + -4d + d2 = 28

Factor a perfect square on the left side:
(d + -2)(d + -2) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(d + -2) equal to 5.291502622 and -5.291502622.


Subproblem 1
d + -2 = 5.291502622

Simplifying
d + -2 = 5.291502622

Reorder the terms:
-2 + d = 5.291502622

Solving
-2 + d = 5.291502622

Solving for variable 'd'.

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

Add '2' to each side of the equation.
-2 + 2 + d = 5.291502622 + 2

Combine like terms: -2 + 2 = 0
0 + d = 5.291502622 + 2
d = 5.291502622 + 2

Combine like terms: 5.291502622 + 2 = 7.291502622
d = 7.291502622

Simplifying
d = 7.291502622


Subproblem 2
d + -2 = -5.291502622

Simplifying
d + -2 = -5.291502622

Reorder the terms:
-2 + d = -5.291502622

Solving
-2 + d = -5.291502622

Solving for variable 'd'.

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

Add '2' to each side of the equation.
-2 + 2 + d = -5.291502622 + 2

Combine like terms: -2 + 2 = 0
0 + d = -5.291502622 + 2
d = -5.291502622 + 2

Combine like terms: -5.291502622 + 2 = -3.291502622
d = -3.291502622

Simplifying
d = -3.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {7.291502622, -3.291502622}

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