0.0114x^2+12.324x+99.66=0

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Solution for 0.0114x^2+12.324x+99.66=0 equation: 


Simplifying
0.0114x2 + 12.324x + 99.66 = 0

Reorder the terms:
99.66 + 12.324x + 0.0114x2 = 0

Solving
99.66 + 12.324x + 0.0114x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.0114 the coefficient of the squared term: 

Divide each side by '0.0114'.
8742.105263 + 1081.052632x + x2 = 0

Move the constant term to the right:

Add '-8742.105263' to each side of the equation.
8742.105263 + 1081.052632x + -8742.105263 + x2 = 0 + -8742.105263

Reorder the terms:
8742.105263 + -8742.105263 + 1081.052632x + x2 = 0 + -8742.105263

Combine like terms: 8742.105263 + -8742.105263 = 0.000000
0.000000 + 1081.052632x + x2 = 0 + -8742.105263
1081.052632x + x2 = 0 + -8742.105263

Combine like terms: 0 + -8742.105263 = -8742.105263
1081.052632x + x2 = -8742.105263

The x term is 1081.052632x.  Take half its coefficient (540.526316).
Square it (292168.6983) and add it to both sides.

Add '292168.6983' to each side of the equation.
1081.052632x + 292168.6983 + x2 = -8742.105263 + 292168.6983

Reorder the terms:
292168.6983 + 1081.052632x + x2 = -8742.105263 + 292168.6983

Combine like terms: -8742.105263 + 292168.6983 = 283426.593037
292168.6983 + 1081.052632x + x2 = 283426.593037

Factor a perfect square on the left side:
(x + 540.526316)(x + 540.526316) = 283426.593037

Calculate the square root of the right side: 532.378242453

Break this problem into two subproblems by setting 
(x + 540.526316) equal to 532.378242453 and -532.378242453.


Subproblem 1
x + 540.526316 = 532.378242453

Simplifying
x + 540.526316 = 532.378242453

Reorder the terms:
540.526316 + x = 532.378242453

Solving
540.526316 + x = 532.378242453

Solving for variable 'x'.

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

Add '-540.526316' to each side of the equation.
540.526316 + -540.526316 + x = 532.378242453 + -540.526316

Combine like terms: 540.526316 + -540.526316 = 0.000000
0.000000 + x = 532.378242453 + -540.526316
x = 532.378242453 + -540.526316

Combine like terms: 532.378242453 + -540.526316 = -8.148073547
x = -8.148073547

Simplifying
x = -8.148073547


Subproblem 2
x + 540.526316 = -532.378242453

Simplifying
x + 540.526316 = -532.378242453

Reorder the terms:
540.526316 + x = -532.378242453

Solving
540.526316 + x = -532.378242453

Solving for variable 'x'.

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

Add '-540.526316' to each side of the equation.
540.526316 + -540.526316 + x = -532.378242453 + -540.526316

Combine like terms: 540.526316 + -540.526316 = 0.000000
0.000000 + x = -532.378242453 + -540.526316
x = -532.378242453 + -540.526316

Combine like terms: -532.378242453 + -540.526316 = -1072.904558453
x = -1072.904558453

Simplifying
x = -1072.904558453


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-8.148073547, -1072.904558453}

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