0.012x^2-0.593x-4.273=0

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Solution for 0.012x^2-0.593x-4.273=0 equation: 


Simplifying
0.012x2 + -0.593x + -4.273 = 0

Reorder the terms:
-4.273 + -0.593x + 0.012x2 = 0

Solving
-4.273 + -0.593x + 0.012x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.012'.
-356.0833333 + -49.41666667x + x2 = 0

Move the constant term to the right:

Add '356.0833333' to each side of the equation.
-356.0833333 + -49.41666667x + 356.0833333 + x2 = 0 + 356.0833333

Reorder the terms:
-356.0833333 + 356.0833333 + -49.41666667x + x2 = 0 + 356.0833333

Combine like terms: -356.0833333 + 356.0833333 = 0.0000000
0.0000000 + -49.41666667x + x2 = 0 + 356.0833333
-49.41666667x + x2 = 0 + 356.0833333

Combine like terms: 0 + 356.0833333 = 356.0833333
-49.41666667x + x2 = 356.0833333

The x term is -49.41666667x.  Take half its coefficient (-24.70833334).
Square it (610.5017364) and add it to both sides.

Add '610.5017364' to each side of the equation.
-49.41666667x + 610.5017364 + x2 = 356.0833333 + 610.5017364

Reorder the terms:
610.5017364 + -49.41666667x + x2 = 356.0833333 + 610.5017364

Combine like terms: 356.0833333 + 610.5017364 = 966.5850697
610.5017364 + -49.41666667x + x2 = 966.5850697

Factor a perfect square on the left side:
(x + -24.70833334)(x + -24.70833334) = 966.5850697

Calculate the square root of the right side: 31.089951266

Break this problem into two subproblems by setting 
(x + -24.70833334) equal to 31.089951266 and -31.089951266.


Subproblem 1
x + -24.70833334 = 31.089951266

Simplifying
x + -24.70833334 = 31.089951266

Reorder the terms:
-24.70833334 + x = 31.089951266

Solving
-24.70833334 + x = 31.089951266

Solving for variable 'x'.

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

Add '24.70833334' to each side of the equation.
-24.70833334 + 24.70833334 + x = 31.089951266 + 24.70833334

Combine like terms: -24.70833334 + 24.70833334 = 0.00000000
0.00000000 + x = 31.089951266 + 24.70833334
x = 31.089951266 + 24.70833334

Combine like terms: 31.089951266 + 24.70833334 = 55.798284606
x = 55.798284606

Simplifying
x = 55.798284606


Subproblem 2
x + -24.70833334 = -31.089951266

Simplifying
x + -24.70833334 = -31.089951266

Reorder the terms:
-24.70833334 + x = -31.089951266

Solving
-24.70833334 + x = -31.089951266

Solving for variable 'x'.

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

Add '24.70833334' to each side of the equation.
-24.70833334 + 24.70833334 + x = -31.089951266 + 24.70833334

Combine like terms: -24.70833334 + 24.70833334 = 0.00000000
0.00000000 + x = -31.089951266 + 24.70833334
x = -31.089951266 + 24.70833334

Combine like terms: -31.089951266 + 24.70833334 = -6.381617926
x = -6.381617926

Simplifying
x = -6.381617926


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {55.798284606, -6.381617926}

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