d^2-13d+2=0

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Solution for d^2-13d+2=0 equation: 


Simplifying
d2 + -13d + 2 = 0

Reorder the terms:
2 + -13d + d2 = 0

Solving
2 + -13d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -13d + -2 + d2 = 0 + -2

Reorder the terms:
2 + -2 + -13d + d2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -13d + d2 = 0 + -2
-13d + d2 = 0 + -2

Combine like terms: 0 + -2 = -2
-13d + d2 = -2

The d term is -13d.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13d + 42.25 + d2 = -2 + 42.25

Reorder the terms:
42.25 + -13d + d2 = -2 + 42.25

Combine like terms: -2 + 42.25 = 40.25
42.25 + -13d + d2 = 40.25

Factor a perfect square on the left side:
(d + -6.5)(d + -6.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(d + -6.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
d + -6.5 = 6.34428877

Simplifying
d + -6.5 = 6.34428877

Reorder the terms:
-6.5 + d = 6.34428877

Solving
-6.5 + d = 6.34428877

Solving for variable 'd'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + d = 6.34428877 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + d = 6.34428877 + 6.5
d = 6.34428877 + 6.5

Combine like terms: 6.34428877 + 6.5 = 12.84428877
d = 12.84428877

Simplifying
d = 12.84428877


Subproblem 2
d + -6.5 = -6.34428877

Simplifying
d + -6.5 = -6.34428877

Reorder the terms:
-6.5 + d = -6.34428877

Solving
-6.5 + d = -6.34428877

Solving for variable 'd'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + d = -6.34428877 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + d = -6.34428877 + 6.5
d = -6.34428877 + 6.5

Combine like terms: -6.34428877 + 6.5 = 0.15571123
d = 0.15571123

Simplifying
d = 0.15571123


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {12.84428877, 0.15571123}

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