0.000579a^2-a+286.25=0

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Solution for 0.000579a^2-a+286.25=0 equation:


Simplifying
0.000579a2 + -1a + 286.25 = 0

Reorder the terms:
286.25 + -1a + 0.000579a2 = 0

Solving
286.25 + -1a + 0.000579a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
0.000579 the coefficient of the squared term: 

Divide each side by '0.000579'.
494386.8739 + -1727.115717a + a2 = 0

Move the constant term to the right:

Add '-494386.8739' to each side of the equation.
494386.8739 + -1727.115717a + -494386.8739 + a2 = 0 + -494386.8739

Reorder the terms:
494386.8739 + -494386.8739 + -1727.115717a + a2 = 0 + -494386.8739

Combine like terms: 494386.8739 + -494386.8739 = 0.0000
0.0000 + -1727.115717a + a2 = 0 + -494386.8739
-1727.115717a + a2 = 0 + -494386.8739

Combine like terms: 0 + -494386.8739 = -494386.8739
-1727.115717a + a2 = -494386.8739

The a term is -1727.115717a.  Take half its coefficient (-863.5578585).
Square it (745732.1750) and add it to both sides.

Add '745732.1750' to each side of the equation.
-1727.115717a + 745732.1750 + a2 = -494386.8739 + 745732.1750

Reorder the terms:
745732.1750 + -1727.115717a + a2 = -494386.8739 + 745732.1750

Combine like terms: -494386.8739 + 745732.1750 = 251345.3011
745732.1750 + -1727.115717a + a2 = 251345.3011

Factor a perfect square on the left side:
(a + -863.5578585)(a + -863.5578585) = 251345.3011

Calculate the square root of the right side: 501.343496118

Break this problem into two subproblems by setting 
(a + -863.5578585) equal to 501.343496118 and -501.343496118.

Subproblem 1

a + -863.5578585 = 501.343496118 Simplifying a + -863.5578585 = 501.343496118 Reorder the terms: -863.5578585 + a = 501.343496118 Solving -863.5578585 + a = 501.343496118 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '863.5578585' to each side of the equation. -863.5578585 + 863.5578585 + a = 501.343496118 + 863.5578585 Combine like terms: -863.5578585 + 863.5578585 = 0.0000000 0.0000000 + a = 501.343496118 + 863.5578585 a = 501.343496118 + 863.5578585 Combine like terms: 501.343496118 + 863.5578585 = 1364.901354618 a = 1364.901354618 Simplifying a = 1364.901354618

Subproblem 2

a + -863.5578585 = -501.343496118 Simplifying a + -863.5578585 = -501.343496118 Reorder the terms: -863.5578585 + a = -501.343496118 Solving -863.5578585 + a = -501.343496118 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '863.5578585' to each side of the equation. -863.5578585 + 863.5578585 + a = -501.343496118 + 863.5578585 Combine like terms: -863.5578585 + 863.5578585 = 0.0000000 0.0000000 + a = -501.343496118 + 863.5578585 a = -501.343496118 + 863.5578585 Combine like terms: -501.343496118 + 863.5578585 = 362.214362382 a = 362.214362382 Simplifying a = 362.214362382

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1364.901354618, 362.214362382}

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