11a^2+10a-31=-12+5a

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Solution for 11a^2+10a-31=-12+5a equation:


Simplifying
11a2 + 10a + -31 = -12 + 5a

Reorder the terms:
-31 + 10a + 11a2 = -12 + 5a

Solving
-31 + 10a + 11a2 = -12 + 5a

Solving for variable 'a'.

Reorder the terms:
-31 + 12 + 10a + -5a + 11a2 = -12 + 5a + 12 + -5a

Combine like terms: -31 + 12 = -19
-19 + 10a + -5a + 11a2 = -12 + 5a + 12 + -5a

Combine like terms: 10a + -5a = 5a
-19 + 5a + 11a2 = -12 + 5a + 12 + -5a

Reorder the terms:
-19 + 5a + 11a2 = -12 + 12 + 5a + -5a

Combine like terms: -12 + 12 = 0
-19 + 5a + 11a2 = 0 + 5a + -5a
-19 + 5a + 11a2 = 5a + -5a

Combine like terms: 5a + -5a = 0
-19 + 5a + 11a2 = 0

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

Divide each side by '11'.
-1.727272727 + 0.4545454545a + a2 = 0

Move the constant term to the right:

Add '1.727272727' to each side of the equation.
-1.727272727 + 0.4545454545a + 1.727272727 + a2 = 0 + 1.727272727

Reorder the terms:
-1.727272727 + 1.727272727 + 0.4545454545a + a2 = 0 + 1.727272727

Combine like terms: -1.727272727 + 1.727272727 = 0.000000000
0.000000000 + 0.4545454545a + a2 = 0 + 1.727272727
0.4545454545a + a2 = 0 + 1.727272727

Combine like terms: 0 + 1.727272727 = 1.727272727
0.4545454545a + a2 = 1.727272727

The a term is 0.4545454545a.  Take half its coefficient (0.2272727273).
Square it (0.05165289257) and add it to both sides.

Add '0.05165289257' to each side of the equation.
0.4545454545a + 0.05165289257 + a2 = 1.727272727 + 0.05165289257

Reorder the terms:
0.05165289257 + 0.4545454545a + a2 = 1.727272727 + 0.05165289257

Combine like terms: 1.727272727 + 0.05165289257 = 1.77892561957
0.05165289257 + 0.4545454545a + a2 = 1.77892561957

Factor a perfect square on the left side:
(a + 0.2272727273)(a + 0.2272727273) = 1.77892561957

Calculate the square root of the right side: 1.333763705

Break this problem into two subproblems by setting 
(a + 0.2272727273) equal to 1.333763705 and -1.333763705.

Subproblem 1

a + 0.2272727273 = 1.333763705 Simplifying a + 0.2272727273 = 1.333763705 Reorder the terms: 0.2272727273 + a = 1.333763705 Solving 0.2272727273 + a = 1.333763705 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + a = 1.333763705 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + a = 1.333763705 + -0.2272727273 a = 1.333763705 + -0.2272727273 Combine like terms: 1.333763705 + -0.2272727273 = 1.1064909777 a = 1.1064909777 Simplifying a = 1.1064909777

Subproblem 2

a + 0.2272727273 = -1.333763705 Simplifying a + 0.2272727273 = -1.333763705 Reorder the terms: 0.2272727273 + a = -1.333763705 Solving 0.2272727273 + a = -1.333763705 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + a = -1.333763705 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + a = -1.333763705 + -0.2272727273 a = -1.333763705 + -0.2272727273 Combine like terms: -1.333763705 + -0.2272727273 = -1.5610364323 a = -1.5610364323 Simplifying a = -1.5610364323

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.1064909777, -1.5610364323}

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