82a^2-38a=279

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Solution for 82a^2-38a=279 equation:


Simplifying
82a2 + -38a = 279

Reorder the terms:
-38a + 82a2 = 279

Solving
-38a + 82a2 = 279

Solving for variable 'a'.

Reorder the terms:
-279 + -38a + 82a2 = 279 + -279

Combine like terms: 279 + -279 = 0
-279 + -38a + 82a2 = 0

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

Divide each side by '82'.
-3.402439024 + -0.4634146341a + a2 = 0

Move the constant term to the right:

Add '3.402439024' to each side of the equation.
-3.402439024 + -0.4634146341a + 3.402439024 + a2 = 0 + 3.402439024

Reorder the terms:
-3.402439024 + 3.402439024 + -0.4634146341a + a2 = 0 + 3.402439024

Combine like terms: -3.402439024 + 3.402439024 = 0.000000000
0.000000000 + -0.4634146341a + a2 = 0 + 3.402439024
-0.4634146341a + a2 = 0 + 3.402439024

Combine like terms: 0 + 3.402439024 = 3.402439024
-0.4634146341a + a2 = 3.402439024

The a term is -0.4634146341a.  Take half its coefficient (-0.2317073171).
Square it (0.05368828080) and add it to both sides.

Add '0.05368828080' to each side of the equation.
-0.4634146341a + 0.05368828080 + a2 = 3.402439024 + 0.05368828080

Reorder the terms:
0.05368828080 + -0.4634146341a + a2 = 3.402439024 + 0.05368828080

Combine like terms: 3.402439024 + 0.05368828080 = 3.4561273048
0.05368828080 + -0.4634146341a + a2 = 3.4561273048

Factor a perfect square on the left side:
(a + -0.2317073171)(a + -0.2317073171) = 3.4561273048

Calculate the square root of the right side: 1.859066245

Break this problem into two subproblems by setting 
(a + -0.2317073171) equal to 1.859066245 and -1.859066245.

Subproblem 1

a + -0.2317073171 = 1.859066245 Simplifying a + -0.2317073171 = 1.859066245 Reorder the terms: -0.2317073171 + a = 1.859066245 Solving -0.2317073171 + a = 1.859066245 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2317073171' to each side of the equation. -0.2317073171 + 0.2317073171 + a = 1.859066245 + 0.2317073171 Combine like terms: -0.2317073171 + 0.2317073171 = 0.0000000000 0.0000000000 + a = 1.859066245 + 0.2317073171 a = 1.859066245 + 0.2317073171 Combine like terms: 1.859066245 + 0.2317073171 = 2.0907735621 a = 2.0907735621 Simplifying a = 2.0907735621

Subproblem 2

a + -0.2317073171 = -1.859066245 Simplifying a + -0.2317073171 = -1.859066245 Reorder the terms: -0.2317073171 + a = -1.859066245 Solving -0.2317073171 + a = -1.859066245 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2317073171' to each side of the equation. -0.2317073171 + 0.2317073171 + a = -1.859066245 + 0.2317073171 Combine like terms: -0.2317073171 + 0.2317073171 = 0.0000000000 0.0000000000 + a = -1.859066245 + 0.2317073171 a = -1.859066245 + 0.2317073171 Combine like terms: -1.859066245 + 0.2317073171 = -1.6273589279 a = -1.6273589279 Simplifying a = -1.6273589279

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.0907735621, -1.6273589279}

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