-0.1x^2+6.6x+8.2=0

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Solution for -0.1x^2+6.6x+8.2=0 equation:


Simplifying
-0.1x2 + 6.6x + 8.2 = 0

Reorder the terms:
8.2 + 6.6x + -0.1x2 = 0

Solving
8.2 + 6.6x + -0.1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.1 the coefficient of the squared term: 

Divide each side by '-0.1'.
-82 + -66x + x2 = 0

Move the constant term to the right:

Add '82' to each side of the equation.
-82 + -66x + 82 + x2 = 0 + 82

Reorder the terms:
-82 + 82 + -66x + x2 = 0 + 82

Combine like terms: -82 + 82 = 0
0 + -66x + x2 = 0 + 82
-66x + x2 = 0 + 82

Combine like terms: 0 + 82 = 82
-66x + x2 = 82

The x term is -66x.  Take half its coefficient (-33).
Square it (1089) and add it to both sides.

Add '1089' to each side of the equation.
-66x + 1089 + x2 = 82 + 1089

Reorder the terms:
1089 + -66x + x2 = 82 + 1089

Combine like terms: 82 + 1089 = 1171
1089 + -66x + x2 = 1171

Factor a perfect square on the left side:
(x + -33)(x + -33) = 1171

Calculate the square root of the right side: 34.219877265

Break this problem into two subproblems by setting 
(x + -33) equal to 34.219877265 and -34.219877265.

Subproblem 1

x + -33 = 34.219877265 Simplifying x + -33 = 34.219877265 Reorder the terms: -33 + x = 34.219877265 Solving -33 + x = 34.219877265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + x = 34.219877265 + 33 Combine like terms: -33 + 33 = 0 0 + x = 34.219877265 + 33 x = 34.219877265 + 33 Combine like terms: 34.219877265 + 33 = 67.219877265 x = 67.219877265 Simplifying x = 67.219877265

Subproblem 2

x + -33 = -34.219877265 Simplifying x + -33 = -34.219877265 Reorder the terms: -33 + x = -34.219877265 Solving -33 + x = -34.219877265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + x = -34.219877265 + 33 Combine like terms: -33 + 33 = 0 0 + x = -34.219877265 + 33 x = -34.219877265 + 33 Combine like terms: -34.219877265 + 33 = -1.219877265 x = -1.219877265 Simplifying x = -1.219877265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {67.219877265, -1.219877265}

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