d^2-133d+36=0

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Solution for d^2-133d+36=0 equation: 


Simplifying
d2 + -133d + 36 = 0

Reorder the terms:
36 + -133d + d2 = 0

Solving
36 + -133d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -133d + -36 + d2 = 0 + -36

Reorder the terms:
36 + -36 + -133d + d2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -133d + d2 = 0 + -36
-133d + d2 = 0 + -36

Combine like terms: 0 + -36 = -36
-133d + d2 = -36

The d term is -133d.  Take half its coefficient (-66.5).
Square it (4422.25) and add it to both sides.

Add '4422.25' to each side of the equation.
-133d + 4422.25 + d2 = -36 + 4422.25

Reorder the terms:
4422.25 + -133d + d2 = -36 + 4422.25

Combine like terms: -36 + 4422.25 = 4386.25
4422.25 + -133d + d2 = 4386.25

Factor a perfect square on the left side:
(d + -66.5)(d + -66.5) = 4386.25

Calculate the square root of the right side: 66.228770183

Break this problem into two subproblems by setting 
(d + -66.5) equal to 66.228770183 and -66.228770183.


Subproblem 1
d + -66.5 = 66.228770183

Simplifying
d + -66.5 = 66.228770183

Reorder the terms:
-66.5 + d = 66.228770183

Solving
-66.5 + d = 66.228770183

Solving for variable 'd'.

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

Add '66.5' to each side of the equation.
-66.5 + 66.5 + d = 66.228770183 + 66.5

Combine like terms: -66.5 + 66.5 = 0.0
0.0 + d = 66.228770183 + 66.5
d = 66.228770183 + 66.5

Combine like terms: 66.228770183 + 66.5 = 132.728770183
d = 132.728770183

Simplifying
d = 132.728770183


Subproblem 2
d + -66.5 = -66.228770183

Simplifying
d + -66.5 = -66.228770183

Reorder the terms:
-66.5 + d = -66.228770183

Solving
-66.5 + d = -66.228770183

Solving for variable 'd'.

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

Add '66.5' to each side of the equation.
-66.5 + 66.5 + d = -66.228770183 + 66.5

Combine like terms: -66.5 + 66.5 = 0.0
0.0 + d = -66.228770183 + 66.5
d = -66.228770183 + 66.5

Combine like terms: -66.228770183 + 66.5 = 0.271229817
d = 0.271229817

Simplifying
d = 0.271229817


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {132.728770183, 0.271229817}

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