19a^2+10a=-11a+4

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Solution for 19a^2+10a=-11a+4 equation:


Simplifying
19a2 + 10a = -11a + 4

Reorder the terms:
10a + 19a2 = -11a + 4

Reorder the terms:
10a + 19a2 = 4 + -11a

Solving
10a + 19a2 = 4 + -11a

Solving for variable 'a'.

Reorder the terms:
-4 + 10a + 11a + 19a2 = 4 + -11a + -4 + 11a

Combine like terms: 10a + 11a = 21a
-4 + 21a + 19a2 = 4 + -11a + -4 + 11a

Reorder the terms:
-4 + 21a + 19a2 = 4 + -4 + -11a + 11a

Combine like terms: 4 + -4 = 0
-4 + 21a + 19a2 = 0 + -11a + 11a
-4 + 21a + 19a2 = -11a + 11a

Combine like terms: -11a + 11a = 0
-4 + 21a + 19a2 = 0

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

Divide each side by '19'.
-0.2105263158 + 1.105263158a + a2 = 0

Move the constant term to the right:

Add '0.2105263158' to each side of the equation.
-0.2105263158 + 1.105263158a + 0.2105263158 + a2 = 0 + 0.2105263158

Reorder the terms:
-0.2105263158 + 0.2105263158 + 1.105263158a + a2 = 0 + 0.2105263158

Combine like terms: -0.2105263158 + 0.2105263158 = 0.0000000000
0.0000000000 + 1.105263158a + a2 = 0 + 0.2105263158
1.105263158a + a2 = 0 + 0.2105263158

Combine like terms: 0 + 0.2105263158 = 0.2105263158
1.105263158a + a2 = 0.2105263158

The a term is 1.105263158a.  Take half its coefficient (0.552631579).
Square it (0.3054016621) and add it to both sides.

Add '0.3054016621' to each side of the equation.
1.105263158a + 0.3054016621 + a2 = 0.2105263158 + 0.3054016621

Reorder the terms:
0.3054016621 + 1.105263158a + a2 = 0.2105263158 + 0.3054016621

Combine like terms: 0.2105263158 + 0.3054016621 = 0.5159279779
0.3054016621 + 1.105263158a + a2 = 0.5159279779

Factor a perfect square on the left side:
(a + 0.552631579)(a + 0.552631579) = 0.5159279779

Calculate the square root of the right side: 0.718281267

Break this problem into two subproblems by setting 
(a + 0.552631579) equal to 0.718281267 and -0.718281267.

Subproblem 1

a + 0.552631579 = 0.718281267 Simplifying a + 0.552631579 = 0.718281267 Reorder the terms: 0.552631579 + a = 0.718281267 Solving 0.552631579 + a = 0.718281267 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.552631579' to each side of the equation. 0.552631579 + -0.552631579 + a = 0.718281267 + -0.552631579 Combine like terms: 0.552631579 + -0.552631579 = 0.000000000 0.000000000 + a = 0.718281267 + -0.552631579 a = 0.718281267 + -0.552631579 Combine like terms: 0.718281267 + -0.552631579 = 0.165649688 a = 0.165649688 Simplifying a = 0.165649688

Subproblem 2

a + 0.552631579 = -0.718281267 Simplifying a + 0.552631579 = -0.718281267 Reorder the terms: 0.552631579 + a = -0.718281267 Solving 0.552631579 + a = -0.718281267 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.552631579' to each side of the equation. 0.552631579 + -0.552631579 + a = -0.718281267 + -0.552631579 Combine like terms: 0.552631579 + -0.552631579 = 0.000000000 0.000000000 + a = -0.718281267 + -0.552631579 a = -0.718281267 + -0.552631579 Combine like terms: -0.718281267 + -0.552631579 = -1.270912846 a = -1.270912846 Simplifying a = -1.270912846

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.165649688, -1.270912846}

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