2x^2+103x+226=0

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Solution for 2x^2+103x+226=0 equation: 


Simplifying
2x2 + 103x + 226 = 0

Reorder the terms:
226 + 103x + 2x2 = 0

Solving
226 + 103x + 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'.
113 + 51.5x + x2 = 0

Move the constant term to the right:

Add '-113' to each side of the equation.
113 + 51.5x + -113 + x2 = 0 + -113

Reorder the terms:
113 + -113 + 51.5x + x2 = 0 + -113

Combine like terms: 113 + -113 = 0
0 + 51.5x + x2 = 0 + -113
51.5x + x2 = 0 + -113

Combine like terms: 0 + -113 = -113
51.5x + x2 = -113

The x term is 51.5x.  Take half its coefficient (25.75).
Square it (663.0625) and add it to both sides.

Add '663.0625' to each side of the equation.
51.5x + 663.0625 + x2 = -113 + 663.0625

Reorder the terms:
663.0625 + 51.5x + x2 = -113 + 663.0625

Combine like terms: -113 + 663.0625 = 550.0625
663.0625 + 51.5x + x2 = 550.0625

Factor a perfect square on the left side:
(x + 25.75)(x + 25.75) = 550.0625

Calculate the square root of the right side: 23.453411266

Break this problem into two subproblems by setting 
(x + 25.75) equal to 23.453411266 and -23.453411266.


Subproblem 1
x + 25.75 = 23.453411266

Simplifying
x + 25.75 = 23.453411266

Reorder the terms:
25.75 + x = 23.453411266

Solving
25.75 + x = 23.453411266

Solving for variable 'x'.

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

Add '-25.75' to each side of the equation.
25.75 + -25.75 + x = 23.453411266 + -25.75

Combine like terms: 25.75 + -25.75 = 0.00
0.00 + x = 23.453411266 + -25.75
x = 23.453411266 + -25.75

Combine like terms: 23.453411266 + -25.75 = -2.296588734
x = -2.296588734

Simplifying
x = -2.296588734


Subproblem 2
x + 25.75 = -23.453411266

Simplifying
x + 25.75 = -23.453411266

Reorder the terms:
25.75 + x = -23.453411266

Solving
25.75 + x = -23.453411266

Solving for variable 'x'.

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

Add '-25.75' to each side of the equation.
25.75 + -25.75 + x = -23.453411266 + -25.75

Combine like terms: 25.75 + -25.75 = 0.00
0.00 + x = -23.453411266 + -25.75
x = -23.453411266 + -25.75

Combine like terms: -23.453411266 + -25.75 = -49.203411266
x = -49.203411266

Simplifying
x = -49.203411266


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.296588734, -49.203411266}

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