0.012x^2-0.583x-4.278=0

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Solution for 0.012x^2-0.583x-4.278=0 equation: 


Simplifying
0.012x2 + -0.583x + -4.278 = 0

Reorder the terms:
-4.278 + -0.583x + 0.012x2 = 0

Solving
-4.278 + -0.583x + 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'.
-356.5 + -48.58333333x + x2 = 0

Move the constant term to the right:

Add '356.5' to each side of the equation.
-356.5 + -48.58333333x + 356.5 + x2 = 0 + 356.5

Reorder the terms:
-356.5 + 356.5 + -48.58333333x + x2 = 0 + 356.5

Combine like terms: -356.5 + 356.5 = 0.0
0.0 + -48.58333333x + x2 = 0 + 356.5
-48.58333333x + x2 = 0 + 356.5

Combine like terms: 0 + 356.5 = 356.5
-48.58333333x + x2 = 356.5

The x term is -48.58333333x.  Take half its coefficient (-24.29166667).
Square it (590.0850696) and add it to both sides.

Add '590.0850696' to each side of the equation.
-48.58333333x + 590.0850696 + x2 = 356.5 + 590.0850696

Reorder the terms:
590.0850696 + -48.58333333x + x2 = 356.5 + 590.0850696

Combine like terms: 356.5 + 590.0850696 = 946.5850696
590.0850696 + -48.58333333x + x2 = 946.5850696

Factor a perfect square on the left side:
(x + -24.29166667)(x + -24.29166667) = 946.5850696

Calculate the square root of the right side: 30.766622655

Break this problem into two subproblems by setting 
(x + -24.29166667) equal to 30.766622655 and -30.766622655.


Subproblem 1
x + -24.29166667 = 30.766622655

Simplifying
x + -24.29166667 = 30.766622655

Reorder the terms:
-24.29166667 + x = 30.766622655

Solving
-24.29166667 + x = 30.766622655

Solving for variable 'x'.

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

Add '24.29166667' to each side of the equation.
-24.29166667 + 24.29166667 + x = 30.766622655 + 24.29166667

Combine like terms: -24.29166667 + 24.29166667 = 0.00000000
0.00000000 + x = 30.766622655 + 24.29166667
x = 30.766622655 + 24.29166667

Combine like terms: 30.766622655 + 24.29166667 = 55.058289325
x = 55.058289325

Simplifying
x = 55.058289325


Subproblem 2
x + -24.29166667 = -30.766622655

Simplifying
x + -24.29166667 = -30.766622655

Reorder the terms:
-24.29166667 + x = -30.766622655

Solving
-24.29166667 + x = -30.766622655

Solving for variable 'x'.

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

Add '24.29166667' to each side of the equation.
-24.29166667 + 24.29166667 + x = -30.766622655 + 24.29166667

Combine like terms: -24.29166667 + 24.29166667 = 0.00000000
0.00000000 + x = -30.766622655 + 24.29166667
x = -30.766622655 + 24.29166667

Combine like terms: -30.766622655 + 24.29166667 = -6.474955985
x = -6.474955985

Simplifying
x = -6.474955985


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {55.058289325, -6.474955985}

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