-2-13.8x=8x(6x+1)

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Solution for -2-13.8x=8x(6x+1) equation:


Simplifying
-2 + -13.8x = 8x(6x + 1)

Reorder the terms:
-2 + -13.8x = 8x(1 + 6x)
-2 + -13.8x = (1 * 8x + 6x * 8x)
-2 + -13.8x = (8x + 48x2)

Solving
-2 + -13.8x = 8x + 48x2

Solving for variable 'x'.

Combine like terms: -13.8x + -8x = -21.8x
-2 + -21.8x + -48x2 = 8x + 48x2 + -8x + -48x2

Reorder the terms:
-2 + -21.8x + -48x2 = 8x + -8x + 48x2 + -48x2

Combine like terms: 8x + -8x = 0
-2 + -21.8x + -48x2 = 0 + 48x2 + -48x2
-2 + -21.8x + -48x2 = 48x2 + -48x2

Combine like terms: 48x2 + -48x2 = 0
-2 + -21.8x + -48x2 = 0

Begin completing the square.  Divide all terms by
-48 the coefficient of the squared term: 

Divide each side by '-48'.
0.04166666667 + 0.4541666667x + x2 = 0

Move the constant term to the right:

Add '-0.04166666667' to each side of the equation.
0.04166666667 + 0.4541666667x + -0.04166666667 + x2 = 0 + -0.04166666667

Reorder the terms:
0.04166666667 + -0.04166666667 + 0.4541666667x + x2 = 0 + -0.04166666667

Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000
0.00000000000 + 0.4541666667x + x2 = 0 + -0.04166666667
0.4541666667x + x2 = 0 + -0.04166666667

Combine like terms: 0 + -0.04166666667 = -0.04166666667
0.4541666667x + x2 = -0.04166666667

The x term is 0.4541666667x.  Take half its coefficient (0.2270833334).
Square it (0.05156684031) and add it to both sides.

Add '0.05156684031' to each side of the equation.
0.4541666667x + 0.05156684031 + x2 = -0.04166666667 + 0.05156684031

Reorder the terms:
0.05156684031 + 0.4541666667x + x2 = -0.04166666667 + 0.05156684031

Combine like terms: -0.04166666667 + 0.05156684031 = 0.00990017364
0.05156684031 + 0.4541666667x + x2 = 0.00990017364

Factor a perfect square on the left side:
(x + 0.2270833334)(x + 0.2270833334) = 0.00990017364

Calculate the square root of the right side: 0.099499616

Break this problem into two subproblems by setting 
(x + 0.2270833334) equal to 0.099499616 and -0.099499616.

Subproblem 1

x + 0.2270833334 = 0.099499616 Simplifying x + 0.2270833334 = 0.099499616 Reorder the terms: 0.2270833334 + x = 0.099499616 Solving 0.2270833334 + x = 0.099499616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2270833334' to each side of the equation. 0.2270833334 + -0.2270833334 + x = 0.099499616 + -0.2270833334 Combine like terms: 0.2270833334 + -0.2270833334 = 0.0000000000 0.0000000000 + x = 0.099499616 + -0.2270833334 x = 0.099499616 + -0.2270833334 Combine like terms: 0.099499616 + -0.2270833334 = -0.1275837174 x = -0.1275837174 Simplifying x = -0.1275837174

Subproblem 2

x + 0.2270833334 = -0.099499616 Simplifying x + 0.2270833334 = -0.099499616 Reorder the terms: 0.2270833334 + x = -0.099499616 Solving 0.2270833334 + x = -0.099499616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2270833334' to each side of the equation. 0.2270833334 + -0.2270833334 + x = -0.099499616 + -0.2270833334 Combine like terms: 0.2270833334 + -0.2270833334 = 0.0000000000 0.0000000000 + x = -0.099499616 + -0.2270833334 x = -0.099499616 + -0.2270833334 Combine like terms: -0.099499616 + -0.2270833334 = -0.3265829494 x = -0.3265829494 Simplifying x = -0.3265829494

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.1275837174, -0.3265829494}

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