11x^2+92x-111=0

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Solution for 11x^2+92x-111=0 equation:


Simplifying
11x2 + 92x + -111 = 0

Reorder the terms:
-111 + 92x + 11x2 = 0

Solving
-111 + 92x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
-10.09090909 + 8.363636364x + x2 = 0

Move the constant term to the right:

Add '10.09090909' to each side of the equation.
-10.09090909 + 8.363636364x + 10.09090909 + x2 = 0 + 10.09090909

Reorder the terms:
-10.09090909 + 10.09090909 + 8.363636364x + x2 = 0 + 10.09090909

Combine like terms: -10.09090909 + 10.09090909 = 0.00000000
0.00000000 + 8.363636364x + x2 = 0 + 10.09090909
8.363636364x + x2 = 0 + 10.09090909

Combine like terms: 0 + 10.09090909 = 10.09090909
8.363636364x + x2 = 10.09090909

The x term is 8.363636364x.  Take half its coefficient (4.181818182).
Square it (17.48760331) and add it to both sides.

Add '17.48760331' to each side of the equation.
8.363636364x + 17.48760331 + x2 = 10.09090909 + 17.48760331

Reorder the terms:
17.48760331 + 8.363636364x + x2 = 10.09090909 + 17.48760331

Combine like terms: 10.09090909 + 17.48760331 = 27.5785124
17.48760331 + 8.363636364x + x2 = 27.5785124

Factor a perfect square on the left side:
(x + 4.181818182)(x + 4.181818182) = 27.5785124

Calculate the square root of the right side: 5.251524769

Break this problem into two subproblems by setting 
(x + 4.181818182) equal to 5.251524769 and -5.251524769.

Subproblem 1

x + 4.181818182 = 5.251524769 Simplifying x + 4.181818182 = 5.251524769 Reorder the terms: 4.181818182 + x = 5.251524769 Solving 4.181818182 + x = 5.251524769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.181818182' to each side of the equation. 4.181818182 + -4.181818182 + x = 5.251524769 + -4.181818182 Combine like terms: 4.181818182 + -4.181818182 = 0.000000000 0.000000000 + x = 5.251524769 + -4.181818182 x = 5.251524769 + -4.181818182 Combine like terms: 5.251524769 + -4.181818182 = 1.069706587 x = 1.069706587 Simplifying x = 1.069706587

Subproblem 2

x + 4.181818182 = -5.251524769 Simplifying x + 4.181818182 = -5.251524769 Reorder the terms: 4.181818182 + x = -5.251524769 Solving 4.181818182 + x = -5.251524769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.181818182' to each side of the equation. 4.181818182 + -4.181818182 + x = -5.251524769 + -4.181818182 Combine like terms: 4.181818182 + -4.181818182 = 0.000000000 0.000000000 + x = -5.251524769 + -4.181818182 x = -5.251524769 + -4.181818182 Combine like terms: -5.251524769 + -4.181818182 = -9.433342951 x = -9.433342951 Simplifying x = -9.433342951

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.069706587, -9.433342951}

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