-11a^2+7a=-166

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Solution for -11a^2+7a=-166 equation:


Simplifying
-11a2 + 7a = -166

Reorder the terms:
7a + -11a2 = -166

Solving
7a + -11a2 = -166

Solving for variable 'a'.

Reorder the terms:
166 + 7a + -11a2 = -166 + 166

Combine like terms: -166 + 166 = 0
166 + 7a + -11a2 = 0

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

Divide each side by '-11'.
-15.09090909 + -0.6363636364a + a2 = 0

Move the constant term to the right:

Add '15.09090909' to each side of the equation.
-15.09090909 + -0.6363636364a + 15.09090909 + a2 = 0 + 15.09090909

Reorder the terms:
-15.09090909 + 15.09090909 + -0.6363636364a + a2 = 0 + 15.09090909

Combine like terms: -15.09090909 + 15.09090909 = 0.00000000
0.00000000 + -0.6363636364a + a2 = 0 + 15.09090909
-0.6363636364a + a2 = 0 + 15.09090909

Combine like terms: 0 + 15.09090909 = 15.09090909
-0.6363636364a + a2 = 15.09090909

The a term is -0.6363636364a.  Take half its coefficient (-0.3181818182).
Square it (0.1012396694) and add it to both sides.

Add '0.1012396694' to each side of the equation.
-0.6363636364a + 0.1012396694 + a2 = 15.09090909 + 0.1012396694

Reorder the terms:
0.1012396694 + -0.6363636364a + a2 = 15.09090909 + 0.1012396694

Combine like terms: 15.09090909 + 0.1012396694 = 15.1921487594
0.1012396694 + -0.6363636364a + a2 = 15.1921487594

Factor a perfect square on the left side:
(a + -0.3181818182)(a + -0.3181818182) = 15.1921487594

Calculate the square root of the right side: 3.897710708

Break this problem into two subproblems by setting 
(a + -0.3181818182) equal to 3.897710708 and -3.897710708.

Subproblem 1

a + -0.3181818182 = 3.897710708 Simplifying a + -0.3181818182 = 3.897710708 Reorder the terms: -0.3181818182 + a = 3.897710708 Solving -0.3181818182 + a = 3.897710708 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + a = 3.897710708 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + a = 3.897710708 + 0.3181818182 a = 3.897710708 + 0.3181818182 Combine like terms: 3.897710708 + 0.3181818182 = 4.2158925262 a = 4.2158925262 Simplifying a = 4.2158925262

Subproblem 2

a + -0.3181818182 = -3.897710708 Simplifying a + -0.3181818182 = -3.897710708 Reorder the terms: -0.3181818182 + a = -3.897710708 Solving -0.3181818182 + a = -3.897710708 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + a = -3.897710708 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + a = -3.897710708 + 0.3181818182 a = -3.897710708 + 0.3181818182 Combine like terms: -3.897710708 + 0.3181818182 = -3.5795288898 a = -3.5795288898 Simplifying a = -3.5795288898

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.2158925262, -3.5795288898}

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