11a^2+19.9a-2.1=0

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Solution for 11a^2+19.9a-2.1=0 equation:


Simplifying
11a2 + 19.9a + -2.1 = 0

Reorder the terms:
-2.1 + 19.9a + 11a2 = 0

Solving
-2.1 + 19.9a + 11a2 = 0

Solving for variable 'a'.

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

Divide each side by '11'.
-0.1909090909 + 1.809090909a + a2 = 0

Move the constant term to the right:

Add '0.1909090909' to each side of the equation.
-0.1909090909 + 1.809090909a + 0.1909090909 + a2 = 0 + 0.1909090909

Reorder the terms:
-0.1909090909 + 0.1909090909 + 1.809090909a + a2 = 0 + 0.1909090909

Combine like terms: -0.1909090909 + 0.1909090909 = 0.0000000000
0.0000000000 + 1.809090909a + a2 = 0 + 0.1909090909
1.809090909a + a2 = 0 + 0.1909090909

Combine like terms: 0 + 0.1909090909 = 0.1909090909
1.809090909a + a2 = 0.1909090909

The a term is 1.809090909a.  Take half its coefficient (0.9045454545).
Square it (0.8182024793) and add it to both sides.

Add '0.8182024793' to each side of the equation.
1.809090909a + 0.8182024793 + a2 = 0.1909090909 + 0.8182024793

Reorder the terms:
0.8182024793 + 1.809090909a + a2 = 0.1909090909 + 0.8182024793

Combine like terms: 0.1909090909 + 0.8182024793 = 1.0091115702
0.8182024793 + 1.809090909a + a2 = 1.0091115702

Factor a perfect square on the left side:
(a + 0.9045454545)(a + 0.9045454545) = 1.0091115702

Calculate the square root of the right side: 1.004545455

Break this problem into two subproblems by setting 
(a + 0.9045454545) equal to 1.004545455 and -1.004545455.

Subproblem 1

a + 0.9045454545 = 1.004545455 Simplifying a + 0.9045454545 = 1.004545455 Reorder the terms: 0.9045454545 + a = 1.004545455 Solving 0.9045454545 + a = 1.004545455 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9045454545' to each side of the equation. 0.9045454545 + -0.9045454545 + a = 1.004545455 + -0.9045454545 Combine like terms: 0.9045454545 + -0.9045454545 = 0.0000000000 0.0000000000 + a = 1.004545455 + -0.9045454545 a = 1.004545455 + -0.9045454545 Combine like terms: 1.004545455 + -0.9045454545 = 0.1000000005 a = 0.1000000005 Simplifying a = 0.1000000005

Subproblem 2

a + 0.9045454545 = -1.004545455 Simplifying a + 0.9045454545 = -1.004545455 Reorder the terms: 0.9045454545 + a = -1.004545455 Solving 0.9045454545 + a = -1.004545455 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9045454545' to each side of the equation. 0.9045454545 + -0.9045454545 + a = -1.004545455 + -0.9045454545 Combine like terms: 0.9045454545 + -0.9045454545 = 0.0000000000 0.0000000000 + a = -1.004545455 + -0.9045454545 a = -1.004545455 + -0.9045454545 Combine like terms: -1.004545455 + -0.9045454545 = -1.9090909095 a = -1.9090909095 Simplifying a = -1.9090909095

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.1000000005, -1.9090909095}

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