19a^2-356a+556=0

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Solution for 19a^2-356a+556=0 equation: 


Simplifying
19a2 + -356a + 556 = 0

Reorder the terms:
556 + -356a + 19a2 = 0

Solving
556 + -356a + 19a2 = 0

Solving for variable 'a'.

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

Divide each side by '19'.
29.26315789 + -18.73684211a + a2 = 0

Move the constant term to the right:

Add '-29.26315789' to each side of the equation.
29.26315789 + -18.73684211a + -29.26315789 + a2 = 0 + -29.26315789

Reorder the terms:
29.26315789 + -29.26315789 + -18.73684211a + a2 = 0 + -29.26315789

Combine like terms: 29.26315789 + -29.26315789 = 0.00000000
0.00000000 + -18.73684211a + a2 = 0 + -29.26315789
-18.73684211a + a2 = 0 + -29.26315789

Combine like terms: 0 + -29.26315789 = -29.26315789
-18.73684211a + a2 = -29.26315789

The a term is -18.73684211a.  Take half its coefficient (-9.368421055).
Square it (87.76731306) and add it to both sides.

Add '87.76731306' to each side of the equation.
-18.73684211a + 87.76731306 + a2 = -29.26315789 + 87.76731306

Reorder the terms:
87.76731306 + -18.73684211a + a2 = -29.26315789 + 87.76731306

Combine like terms: -29.26315789 + 87.76731306 = 58.50415517
87.76731306 + -18.73684211a + a2 = 58.50415517

Factor a perfect square on the left side:
(a + -9.368421055)(a + -9.368421055) = 58.50415517

Calculate the square root of the right side: 7.648800898

Break this problem into two subproblems by setting 
(a + -9.368421055) equal to 7.648800898 and -7.648800898.


Subproblem 1
a + -9.368421055 = 7.648800898

Simplifying
a + -9.368421055 = 7.648800898

Reorder the terms:
-9.368421055 + a = 7.648800898

Solving
-9.368421055 + a = 7.648800898

Solving for variable 'a'.

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

Add '9.368421055' to each side of the equation.
-9.368421055 + 9.368421055 + a = 7.648800898 + 9.368421055

Combine like terms: -9.368421055 + 9.368421055 = 0.000000000
0.000000000 + a = 7.648800898 + 9.368421055
a = 7.648800898 + 9.368421055

Combine like terms: 7.648800898 + 9.368421055 = 17.017221953
a = 17.017221953

Simplifying
a = 17.017221953


Subproblem 2
a + -9.368421055 = -7.648800898

Simplifying
a + -9.368421055 = -7.648800898

Reorder the terms:
-9.368421055 + a = -7.648800898

Solving
-9.368421055 + a = -7.648800898

Solving for variable 'a'.

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

Add '9.368421055' to each side of the equation.
-9.368421055 + 9.368421055 + a = -7.648800898 + 9.368421055

Combine like terms: -9.368421055 + 9.368421055 = 0.000000000
0.000000000 + a = -7.648800898 + 9.368421055
a = -7.648800898 + 9.368421055

Combine like terms: -7.648800898 + 9.368421055 = 1.719620157
a = 1.719620157

Simplifying
a = 1.719620157


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {17.017221953, 1.719620157}

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