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

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


Simplifying
-314.011706x2 + 1x + 24672.00111525761 = 0

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

Solving
24672.00111525761 + 1x + -314.011706x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-314.011706 the coefficient of the squared term: 

Divide each side by '-314.011706'.
-78.57032284 + -0.003184594653x + x2 = 0

Move the constant term to the right:

Add '78.57032284' to each side of the equation.
-78.57032284 + -0.003184594653x + 78.57032284 + x2 = 0 + 78.57032284

Reorder the terms:
-78.57032284 + 78.57032284 + -0.003184594653x + x2 = 0 + 78.57032284

Combine like terms: -78.57032284 + 78.57032284 = 0.00000000
0.00000000 + -0.003184594653x + x2 = 0 + 78.57032284
-0.003184594653x + x2 = 0 + 78.57032284

Combine like terms: 0 + 78.57032284 = 78.57032284
-0.003184594653x + x2 = 78.57032284

The x term is -0.003184594653x.  Take half its coefficient (-0.001592297327).
Square it (0.000002535410778) and add it to both sides.

Add '0.000002535410778' to each side of the equation.
-0.003184594653x + 0.000002535410778 + x2 = 78.57032284 + 0.000002535410778

Reorder the terms:
0.000002535410778 + -0.003184594653x + x2 = 78.57032284 + 0.000002535410778

Combine like terms: 78.57032284 + 0.000002535410778 = 78.570325375410778
0.000002535410778 + -0.003184594653x + x2 = 78.570325375410778

Factor a perfect square on the left side:
(x + -0.001592297327)(x + -0.001592297327) = 78.570325375410778

Calculate the square root of the right side: 8.863990375

Break this problem into two subproblems by setting 
(x + -0.001592297327) equal to 8.863990375 and -8.863990375.


Subproblem 1
x + -0.001592297327 = 8.863990375

Simplifying
x + -0.001592297327 = 8.863990375

Reorder the terms:
-0.001592297327 + x = 8.863990375

Solving
-0.001592297327 + x = 8.863990375

Solving for variable 'x'.

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

Add '0.001592297327' to each side of the equation.
-0.001592297327 + 0.001592297327 + x = 8.863990375 + 0.001592297327

Combine like terms: -0.001592297327 + 0.001592297327 = 0.000000000000
0.000000000000 + x = 8.863990375 + 0.001592297327
x = 8.863990375 + 0.001592297327

Combine like terms: 8.863990375 + 0.001592297327 = 8.865582672327
x = 8.865582672327

Simplifying
x = 8.865582672327


Subproblem 2
x + -0.001592297327 = -8.863990375

Simplifying
x + -0.001592297327 = -8.863990375

Reorder the terms:
-0.001592297327 + x = -8.863990375

Solving
-0.001592297327 + x = -8.863990375

Solving for variable 'x'.

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

Add '0.001592297327' to each side of the equation.
-0.001592297327 + 0.001592297327 + x = -8.863990375 + 0.001592297327

Combine like terms: -0.001592297327 + 0.001592297327 = 0.000000000000
0.000000000000 + x = -8.863990375 + 0.001592297327
x = -8.863990375 + 0.001592297327

Combine like terms: -8.863990375 + 0.001592297327 = -8.862398077673
x = -8.862398077673

Simplifying
x = -8.862398077673


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.865582672327, -8.862398077673}

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