2x^2+41x+66=0

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Solution for 2x^2+41x+66=0 equation: 


Simplifying
2x2 + 41x + 66 = 0

Reorder the terms:
66 + 41x + 2x2 = 0

Solving
66 + 41x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
33 + 20.5x + x2 = 0

Move the constant term to the right:

Add '-33' to each side of the equation.
33 + 20.5x + -33 + x2 = 0 + -33

Reorder the terms:
33 + -33 + 20.5x + x2 = 0 + -33

Combine like terms: 33 + -33 = 0
0 + 20.5x + x2 = 0 + -33
20.5x + x2 = 0 + -33

Combine like terms: 0 + -33 = -33
20.5x + x2 = -33

The x term is 20.5x.  Take half its coefficient (10.25).
Square it (105.0625) and add it to both sides.

Add '105.0625' to each side of the equation.
20.5x + 105.0625 + x2 = -33 + 105.0625

Reorder the terms:
105.0625 + 20.5x + x2 = -33 + 105.0625

Combine like terms: -33 + 105.0625 = 72.0625
105.0625 + 20.5x + x2 = 72.0625

Factor a perfect square on the left side:
(x + 10.25)(x + 10.25) = 72.0625

Calculate the square root of the right side: 8.488963423

Break this problem into two subproblems by setting 
(x + 10.25) equal to 8.488963423 and -8.488963423.


Subproblem 1
x + 10.25 = 8.488963423

Simplifying
x + 10.25 = 8.488963423

Reorder the terms:
10.25 + x = 8.488963423

Solving
10.25 + x = 8.488963423

Solving for variable 'x'.

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

Add '-10.25' to each side of the equation.
10.25 + -10.25 + x = 8.488963423 + -10.25

Combine like terms: 10.25 + -10.25 = 0.00
0.00 + x = 8.488963423 + -10.25
x = 8.488963423 + -10.25

Combine like terms: 8.488963423 + -10.25 = -1.761036577
x = -1.761036577

Simplifying
x = -1.761036577


Subproblem 2
x + 10.25 = -8.488963423

Simplifying
x + 10.25 = -8.488963423

Reorder the terms:
10.25 + x = -8.488963423

Solving
10.25 + x = -8.488963423

Solving for variable 'x'.

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

Add '-10.25' to each side of the equation.
10.25 + -10.25 + x = -8.488963423 + -10.25

Combine like terms: 10.25 + -10.25 = 0.00
0.00 + x = -8.488963423 + -10.25
x = -8.488963423 + -10.25

Combine like terms: -8.488963423 + -10.25 = -18.738963423
x = -18.738963423

Simplifying
x = -18.738963423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.761036577, -18.738963423}

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