-24672.00111525761x^2+1x+314.011706=0

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Solution for -24672.00111525761x^2+1x+314.011706=0 equation: 


Simplifying
-24672.00111525761x2 + 1x + 314.011706 = 0

Reorder the terms:
314.011706 + 1x + -24672.00111525761x2 = 0

Solving
314.011706 + 1x + -24672.00111525761x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-24672.00111525761 the coefficient of the squared term: 

Divide each side by '-24672.00111525761'.
-0.01272745184 + -0.00004053177508x + x2 = 0

Move the constant term to the right:

Add '0.01272745184' to each side of the equation.
-0.01272745184 + -0.00004053177508x + 0.01272745184 + x2 = 0 + 0.01272745184

Reorder the terms:
-0.01272745184 + 0.01272745184 + -0.00004053177508x + x2 = 0 + 0.01272745184

Combine like terms: -0.01272745184 + 0.01272745184 = 0.00000000000
0.00000000000 + -0.00004053177508x + x2 = 0 + 0.01272745184
-0.00004053177508x + x2 = 0 + 0.01272745184

Combine like terms: 0 + 0.01272745184 = 0.01272745184
-0.00004053177508x + x2 = 0.01272745184

The x term is -0.00004053177508x.  Take half its coefficient (-0.00002026588754).
Square it (0.0000000004107061978) and add it to both sides.

Add '0.0000000004107061978' to each side of the equation.
-0.00004053177508x + 0.0000000004107061978 + x2 = 0.01272745184 + 0.0000000004107061978

Reorder the terms:
0.0000000004107061978 + -0.00004053177508x + x2 = 0.01272745184 + 0.0000000004107061978

Combine like terms: 0.01272745184 + 0.0000000004107061978 = 0.0127274522507061978
0.0000000004107061978 + -0.00004053177508x + x2 = 0.0127274522507061978

Factor a perfect square on the left side:
(x + -0.00002026588754)(x + -0.00002026588754) = 0.0127274522507061978

Calculate the square root of the right side: 0.112816011

Break this problem into two subproblems by setting 
(x + -0.00002026588754) equal to 0.112816011 and -0.112816011.


Subproblem 1
x + -0.00002026588754 = 0.112816011

Simplifying
x + -0.00002026588754 = 0.112816011

Reorder the terms:
-0.00002026588754 + x = 0.112816011

Solving
-0.00002026588754 + x = 0.112816011

Solving for variable 'x'.

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

Add '0.00002026588754' to each side of the equation.
-0.00002026588754 + 0.00002026588754 + x = 0.112816011 + 0.00002026588754

Combine like terms: -0.00002026588754 + 0.00002026588754 = 0.00000000000000
0.00000000000000 + x = 0.112816011 + 0.00002026588754
x = 0.112816011 + 0.00002026588754

Combine like terms: 0.112816011 + 0.00002026588754 = 0.11283627688754
x = 0.11283627688754

Simplifying
x = 0.11283627688754


Subproblem 2
x + -0.00002026588754 = -0.112816011

Simplifying
x + -0.00002026588754 = -0.112816011

Reorder the terms:
-0.00002026588754 + x = -0.112816011

Solving
-0.00002026588754 + x = -0.112816011

Solving for variable 'x'.

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

Add '0.00002026588754' to each side of the equation.
-0.00002026588754 + 0.00002026588754 + x = -0.112816011 + 0.00002026588754

Combine like terms: -0.00002026588754 + 0.00002026588754 = 0.00000000000000
0.00000000000000 + x = -0.112816011 + 0.00002026588754
x = -0.112816011 + 0.00002026588754

Combine like terms: -0.112816011 + 0.00002026588754 = -0.11279574511246
x = -0.11279574511246

Simplifying
x = -0.11279574511246


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.11283627688754, -0.11279574511246}

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