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

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


Simplifying
-24672.00111525761x2 + 314.011706x + 1 = 0

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

Solving
1 + 314.011706x + -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'.
-0.00004053177508 + -0.01272745184x + x2 = 0

Move the constant term to the right:

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

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

Combine like terms: -0.00004053177508 + 0.00004053177508 = 0.00000000000000
0.00000000000000 + -0.01272745184x + x2 = 0 + 0.00004053177508
-0.01272745184x + x2 = 0 + 0.00004053177508

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

The x term is -0.01272745184x.  Take half its coefficient (-0.00636372592).
Square it (0.00004049700758) and add it to both sides.

Add '0.00004049700758' to each side of the equation.
-0.01272745184x + 0.00004049700758 + x2 = 0.00004053177508 + 0.00004049700758

Reorder the terms:
0.00004049700758 + -0.01272745184x + x2 = 0.00004053177508 + 0.00004049700758

Combine like terms: 0.00004053177508 + 0.00004049700758 = 0.00008102878266
0.00004049700758 + -0.01272745184x + x2 = 0.00008102878266

Factor a perfect square on the left side:
(x + -0.00636372592)(x + -0.00636372592) = 0.00008102878266

Calculate the square root of the right side: 0.009001599

Break this problem into two subproblems by setting 
(x + -0.00636372592) equal to 0.009001599 and -0.009001599.

Subproblem 1

x + -0.00636372592 = 0.009001599 Simplifying x + -0.00636372592 = 0.009001599 Reorder the terms: -0.00636372592 + x = 0.009001599 Solving -0.00636372592 + x = 0.009001599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00636372592' to each side of the equation. -0.00636372592 + 0.00636372592 + x = 0.009001599 + 0.00636372592 Combine like terms: -0.00636372592 + 0.00636372592 = 0.00000000000 0.00000000000 + x = 0.009001599 + 0.00636372592 x = 0.009001599 + 0.00636372592 Combine like terms: 0.009001599 + 0.00636372592 = 0.01536532492 x = 0.01536532492 Simplifying x = 0.01536532492

Subproblem 2

x + -0.00636372592 = -0.009001599 Simplifying x + -0.00636372592 = -0.009001599 Reorder the terms: -0.00636372592 + x = -0.009001599 Solving -0.00636372592 + x = -0.009001599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00636372592' to each side of the equation. -0.00636372592 + 0.00636372592 + x = -0.009001599 + 0.00636372592 Combine like terms: -0.00636372592 + 0.00636372592 = 0.00000000000 0.00000000000 + x = -0.009001599 + 0.00636372592 x = -0.009001599 + 0.00636372592 Combine like terms: -0.009001599 + 0.00636372592 = -0.00263787308 x = -0.00263787308 Simplifying x = -0.00263787308

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.01536532492, -0.00263787308}

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